Jean-Marc Salotti
email: jean-marc.salotti@ensc.fr

Julien Doche

RESCUE SYSTEMS FOR MARS LANDING

Keywords: Entry, descent and landing, backup strategies, landing risks

published or not. The documents may come

Preliminary study of rescue systems for Mars landing

Introduction

As entry, descent and landing (EDL) on Mars is one of the most dangerous phases of a human mission to Mars, is it necessary to integrate back-up systems to reduce the risk of losing astronauts [START_REF] Braun | Mars Entry, Descent and Landing Challenges[END_REF][START_REF] Christian | Sizing of an Entry, Descent, and Landing System for Human Mars Exploration[END_REF][START_REF] Cruz | Entry, descent, and landing technology concept trade study for increasing payload mass to the surface of Mars[END_REF]? On Earth, the launch and access to orbit phases, which require heavy and complex propulsion systems are considered very risky. In order to mitigate the risks, the human rated qualification rule is to provide an emergency evacuation system that can be triggered at any time for a safe return to the ground under parachutes. For the return from Earth orbit, no emergency system is available, apart from the redundancy of the parachutes, but there is however no need for a propulsion system (except during the last second for the final cushioning). As the atmosphere of Mars is much thinner than Earth's, a propulsive phase is required for the last braking and, as the surface is irregular, the propulsive phase might involve lateral moves as was the case for the Apollo 11 mission to the Moon. The complexity of the EDL phase for Mars is therefore much greater than Earth's and the inclusion of a backup system for landing is an important issue. A possible solution is to impose a constraint on the architecture of the mission, such that the stay on the surface is relatively short and the crewed descent vehicle includes a fully fuelled Mars ascent vehicle [START_REF] Connelly | report of the Fifth Community Workshop on Achievability and Sustainability of Human Exploration of Mars (AM V Report)[END_REF][START_REF] Price | Sortie-Class Human Missions to Mars[END_REF]. A NASA team proposed another solution with a single-stage reusable vehicle called Hercules [START_REF] Komar | Lunar and Mars Ascent and Descent/Entry Crew Abort Modes for the Hercules Single-Stage Reusable Vehicle[END_REF]. These strategies allow an abort to orbit mode. In addition, if the crew is embedded in a small capsule with its own propulsion capabilities, an abort to surface mode is also possible [START_REF] Komar | Lunar and Mars Ascent and Descent/Entry Crew Abort Modes for the Hercules Single-Stage Reusable Vehicle[END_REF]. If these constraints are not accepted, it is difficult to implement abort options without important mass penalties, which could imply additional heavy launches from Earth and complex LEO assembly operations. Any backup system must be very light to be acceptable. Interestingly, during Gemini missions, astronauts were equipped with a parachute and could eject [START_REF] Ray | Development and Qualification of Gemini Escape System[END_REF]. Likewise, when the Hermès shuttle was designed, seat ejection systems were planned, similar to those used for military airplanes [START_REF] Colrat | Hermes Escape System[END_REF][START_REF] Shayler | Space Rescue[END_REF]. Is it possible to use ejection seats for Mars landings? And if yes, what would be the conditions of use and the requirements for complementary systems allowing safe landing and survival after landing? These questions are addressed in the following sections. In section 2, the risks of the EDL phase are summarised. Section 3 is dedicated to the constraints and conditions that have to be fulfilled to enable the rescue of the astronauts. Different rescue systems are proposed and discussed in Section 4 and the main conclusions are given in the final section.

EDL risks

Numerous robotic missions have been implemented for the exploration of the surface of Mars. Many have been successful (Viking, Pathfinder, Mer, Phenix, Curiosity, Insight), but many others failed to reach the surface at the very end of the mission, due to a problem encountered during the EDL phase, see Table 1. If EDL risks are considered very high for robotic missions, it could be even worse for human missions. Many authors highlighted these risks, explaining that landing heavy vehicles on Mars is more challenging than landing light vehicles [START_REF] Braun | Mars Entry, Descent and Landing Challenges[END_REF][START_REF] Christian | Sizing of an Entry, Descent, and Landing System for Human Mars Exploration[END_REF][START_REF] Cruz | Entry, descent, and landing technology concept trade study for increasing payload mass to the surface of Mars[END_REF][START_REF] Kurzun | A concept for the entry, descent, and landing of high-mass payloads at Mars[END_REF][START_REF] Drake | Reference Mission Version 3.0 Addendum to the Human Exploration of Mars: The Reference Mission of the NASA Mars Exploration Study[END_REF][START_REF] Salotti | Revised Scenario for Human Missions to Mars[END_REF][START_REF] Genta | IAA Study Group 3.16: Cosmic Study on Global Human Mars System Missions Exploration[END_REF]. There are several reasons for this:

• The ballistic coefficient is in general higher for heavy vehicles, which means that atmospheric braking is less efficient. • As the use of gigantic parachutes would be impractical, different EDL systems must be considered for heavy vehicles, for instance giant inflatable heat shields [START_REF] Drake | Mars Architecture Steering Group, Human Exploration of Mars[END_REF], with a low Technology Readiness Level. • If very large diameter heat shields are required (perhaps two heat shields, one for the hypersonic and another for the supersonic regime), a complex deployment procedure would need to be carried out. • At the end of the atmospheric braking phase, heat shields may have to be ejected, which might be difficult.

• After heat shield ejection, the vehicle must be reoriented in a very short time so that the thrust direction is opposed to the speed direction. This manoeuvre is more difficult and takes longer for large vehicles. • For the final propulsion phase, multiple rocket engines have to be fired at supersonic regime.

• The velocity and the landing position must be controlled with greater accuracy.

All in all, according to NASA, EDL risks are considered a major concern of human missions to Mars and the best option remains to be determined [START_REF] Drake | Reference Mission Version 3.0 Addendum to the Human Exploration of Mars: The Reference Mission of the NASA Mars Exploration Study[END_REF][START_REF] Drake | Mars Architecture Steering Group, Human Exploration of Mars[END_REF].

Top level functions

Main principles

The rescue system must be composed of four major subsystems, the evacuation system (ES), the descent and landing system (DLS), the surface rescue system (SRS) and the communication system (CS). The top level functions are: F1: Phase 1, evacuation: Use the ES to rapidly evacuate the astronauts from the spacecraft. F2: Phase 2a, descent: Use the DLS to provide an alternative and safe descent system to reach the surface (it is assumed that coming back to orbit is practically impossible). F3: Phase 2b, landing: Use the DLS to provide a physiologically safe landing, including lateral adjustments to avoid dangerous zones (e.g. edge of a cliff). F4: Phase 2c, exit: Provide a safe exit from the DLS. F5: Phase 3, surface mobility: Use the SRS to provide transportation means to the astronauts once landed on the surface, so that they can reach a safe haven. F6: Phase 2 and 3, life support: Provide a life support system during the descent and on the surface for a minimum duration of at least 8 hours (to be discussed). This life support system may be associated to the DLS or SRS, or both. F7: Phase 3, communication: Use the CS to provide communication capabilities with mission control, and all other astronauts in the mission and any other automatic system involved in the rescue (SRS) in order to define and share the best rescue strategy. F8: Phase 3, navigation: Provide navigation capabilities to the astronaut, position and orientation, to determine the direction and distance of the closest safe haven. F9: Phase 4, safe haven. Complementary assets must be present on the surface in order to carry on or abort the mission safely, eventually with restrictive operational conditions (to be discussed). In particular, a habitable module must be present on the surface before the arrival of the astronauts. It is an important element of the SRS.

In addition, the rescue system on board the landing vehicle (ES and DLS) must be as simple and light as possible, to avoid the complexification of the primary EDL system and the complexification of the mission architecture.

Assessment of the different options

Several options are possible for the evacuation and descent and landing systems (ES and DLS):

1) Ejection of a small vehicle (capsule): As is proposed for take-off from Earth, all astronauts can be placed in a small capsule that can be ejected in an emergency procedure, thanks to pyrotechnic systems and a propulsion system. However, even if a parachute could help braking before landing, as the density of the atmosphere is very low, it would not be sufficient to reduce the velocity to acceptable levels and to land safely on Mars. A heavy propulsion system would thus be required, which would be a serious mass penalty for the vehicle and a handicap for the design of the primary EDL system. As this is contrary to our recommendations, another option would be preferable. 2) Ejection seat with spacesuit and parachute [START_REF] Shayler | Space Rescue[END_REF]: This option has already been implemented for the Vostok and the Gemini programs (see Fig. 1). It was also considered and validated for the European Hermes shuttle, which remained a concept study [START_REF] Colrat | Hermes Escape System[END_REF]. For Mars, the idea is to trigger a pyrotechnic system that would open the wall of the space vehicle and allow the ejection of the astronauts on their seats. Importantly, implementing that ejection system will require the crew to land in an EVA-ready suit, portable life support system included, eventually not on their back but attached to the seat. Such an option would be viable during a short window of time at the end of the atmospheric braking, when the vehicle has been slowed down to acceptable velocities. Once ejected, a parachute immediately opens and progressively reduces the speed of the astronaut. On Earth, thanks to appropriate parachute systems (disk gap band parachute), ejection seats can be used at very high velocities, typically around Mach 1 at sea level. On Mars, as atmospheric pressure is much lower, parachutes could be opened at much higher velocities. According to Braun and Manning, on Mars, taking thermal constraints into account, it would be possible to use parachutes at Mach 2.7 or even Mach 3 [START_REF] Braun | Mars Entry, Descent and Landing Challenges[END_REF]. On Earth, the final (and relatively safe) velocity of a parachutist is between 5 and 8 m/s. On Mars, even if very large parachutes were used, the final falling velocity would be around 50 m/s, which would kill the astronaut at impact. Another system is therefore required to reduce the velocity at touch down. Three main options are possible for the landing subsystem of the DLS: a. Airbag: An inflatable system could absorb the energy at impact. However, if the final descent velocity is of the order of 50 m/s, it must be very large to reduce accelerations to acceptable physiological levels. For instance, if the maximum allowed acceleration is 10g, the airbag must be at least 12.5 metres high, which is impractical. This option is rejected. b. Backpack jetpack: If backpack jetpacks are used, the astronauts land on their feet. The thrusters of the jetpack can be controlled in an automatic way. However, after an interplanetary flight without gravity, it is doubtful that the astronauts could easily stand on the surface. In addition, the trauma of the ejection might cause a loss of consciousness, which would be dangerous in case of landing in a standing position. This option is therefore also rejected. c. Ejection seat equipped with thrusters: The astronaut remains in the seat until touch down. Small thrusters are positioned under the seat. After ejection, a parachute is used for the main braking phase.

Then thrusters are used at the very end of the descent to land softly on the surface. d. Same as option c, but a skycrane is used: This technology was justified by NASA to facilitate the deployment of rovers on the surface of Mars (e.g., Curiosity). There was indeed no need to add a descent platform and the ground was not impacted by the exhaust of the thrusters. However, in the context of the rescue system, there is no clear advantage for a skycrane, which is complex to deploy and not the lighter option. Option 2c is therefore the preferred option. This concept is illustrated in Fig. 2.

After landing

Once on the surface, it is the role of the SRS to rescue the astronauts. Other resources should be available, such as a habitable module to make sure that the astronauts can reach a safe haven. In most Mars mission architectures, such a habitable module is indeed pre-positioned on Mars before the astronauts' arrival [START_REF] Genta | IAA Study Group 3.16: Cosmic Study on Global Human Mars System Missions Exploration[END_REF][START_REF] Drake | Mars Architecture Steering Group, Human Exploration of Mars[END_REF][START_REF] Salotti | Robust, affordable, semi-direct Mars mission[END_REF][START_REF] Zubrin | Mars Direct: Humans to the Red Planet by[END_REF]. In nominal conditions, there is an accurate control of the descent and the landing ellipse is of the order of 10 kilometres large at the end of the aerodynamic braking [START_REF] Wolf | Performance trades for Mars pinpoint landing[END_REF]. According to a NASA study, a lateral displacement of a few kilometres is planned to reach the base in a precise way [START_REF] Drake | Mars Architecture Steering Group, Human Exploration of Mars[END_REF]. If the descent goes badly, but the navigation is correct, the distance of the landing site is thus of the order of 10 km, which seems feasible walking. If on the other hand the navigation is affected, the distance can be enormous, which would certainly condemn the survival astronauts. It is assumed in the following that a habitable module is already present on the surface and is a fundamental element of any rescue system.

There are three transportation options to reach the habitable module: 1) Astronaut walking. After several months in 0g, without countermeasures, the crew members will be deconditioned and will have difficulties standing and walking. This is a well-known problem and two options are generally considered to avoid or mitigate the effects. The first is a simulation of the gravity by a permanent rotation of two modules and the second is the daily use of a small centrifuge [START_REF] Braddock | Artificial gravity: small steps on the journey to the giant leap[END_REF]. Whatever the option, the astronauts will use exercise machines to stay fit. It is therefore expected that the crew members will still have some walking capabilities upon arrival, though probably less than nominal as a period of sensorimotor adaptation might also be required. An important issue is the adaptation of the spacesuit to long distance walking. Several spacesuit designs are currently investigated at NASA [START_REF] Mr | US Spacesuits[END_REF][START_REF] Abercromby | Crew Health and Performance Extravehicular Activity Roadmap: 2020[END_REF]. Operational tests will determine the physical and cognitive effects of 3x8 hour simulated planetary EVA in a week. Such spacesuits are nevertheless heavy and not optimized for walking. Another concept, the bio-suit, might be more appropriate [START_REF] Pitts | Astronaut Bio-Suit for Exploration Class Missions[END_REF]. On Earth, the walking speed can be as high as 5.5 km/h without much effort. Some research suggests that the optimum walking speed on Mars would be around 3.4km/h [START_REF] Cavagna | Walking on Mars[END_REF]. This optimum is lower on Mars because it takes more time for the centre of mass to come down and therefore for the front foot to come back to the ground. However, as the mass of the astronaut would be lower on Mars, even wearing a spacesuit, an adaptive walk or a fast walk would certainly be easier on Mars than on Earth. Aldrin reported, for instance for the Moon, that walking like we do on Earth was not efficient but that he was able to make small jumps and to reach 5 to 6 miles per hour without effort [23]. During extra-vehicular activity outside the International Space Station, the autonomy of life support systems is limited by lithium hydroxide canisters for the removal of carbon dioxide. Future technologies might provide an autonomy of 8 hours [START_REF] Abercromby | Crew Health and Performance Extravehicular Activity Roadmap: 2020[END_REF][START_REF] Heather | Development of a Rapid Cycling CO2 and H2O Removal Sorbent[END_REF]. Providing that an effort is made to mitigate 0g effects and to adapt the spacesuit, walking would be the first option to reach the habitable module [START_REF] Braddock | Artificial gravity: small steps on the journey to the giant leap[END_REF][START_REF] Lee | Efficacy of Gradient Compression Garments in the Hours After Long-Duration Spaceflight[END_REF][START_REF] Porter | Soft Exoskeleton Knee Prototype for Advanced Space Suits and Planetary Exploration[END_REF]. This is however not possible if the module is too far. Another option must be preferred for adapting to a greater number of possible situations.

2) The seat is equipped with wheels and is transformed into an unpressurized rover. This option is possible, but it increases the mass of the rescue system and there is no guarantee that, first, the landing zone allows driving a rover (imagine a scree) and, secondly, that a safe path exists towards the habitable module (no impassable obstacle, e.g., landing on the other side of a very long and deep canyon). 3) A vehicle is present near the habitat and is used to bring the astronauts back to it. Importantly, at least for the first missions to Mars, it is expected that there will be no rescue team on the surface. As a consequence, any rescue vehicle must be automatically deployed and remotely driven towards the landing zone. Option 3) is the preferred option. Several categories of vehicle can be used for the rescue: pressurised or not, fully automatic, remotely controlled, or possibly with the two operating modes, depending on the context. According to a previous study, the choice between a pressurised rover and an unpressurised one (or several unpressurised rovers if there are several astronauts) is difficult, see Table 2 [START_REF] Hoffman | The Mars Surface Reference Mission: A Description of Human and Robotic Surface Activities[END_REF][START_REF] Salotti | Small rover exploration capabilities[END_REF]. According to our assessment, both options provide acceptable rescue solutions. The choice could be in fact made according to criteria linked to the scientific objectives of the mission. The only constraint is to have the vehicle(s) deployed on the surface ready for a rescue before the arrival of the astronauts. Regarding the operating mode, the best trade-off could be automatic as long as the astronaut does not take control of the vehicle and command it remotely.

Life support system

The astronauts must wear an EVA-suit equipped with a life support system. After landing, the astronauts would have to leave their seat. It is conceivable that among the elements making up the ejection system is a module that can be pressurised (this can take a simple form such as a tent). With the help of this shelter, if the astronauts can remove their suit, they will be able to repair it more easily but also to care for themselves and replace various essential elements of the suits, such as oxygen reserves and carbon dioxide filters. The pressurised shelter also provides water and food supplies outside the suit. Depending on the complexity of the pressurised module, it can be used to manage temperature variations. Indeed, the temperature variations on the surface of Mars are important, going from -125°C to +20°C.

Without this additional pressurised space, the astronauts have to rely solely on the resources of the life support systems attached to the suits. NASA is currently designing and testing EVA-suits for the Moon and Mars with an autonomy of 8 hours [START_REF] Abercromby | Crew Health and Performance Extravehicular Activity Roadmap: 2020[END_REF]. If the suits used on Mars evolve, with significant improvements on the astronaut's mobility and the quality of the communication systems, the oxygen autonomy should remain similar due to constraints on the size and mass of the reserves. The only accessible food and water reserves are those already present in the suit. Healing and repairing are also more difficult.

Whether or not a base is already present on Mars with other astronauts, communicating with the habitable module and the rescue vehicle(s) is fundamental. Thus, in order to maximize the survival probability, the evacuation seat must contain a radio communication system to be able to start the rescue procedure with the vehicles. In case of injuries during the descent and landing on Mars, the crew will have to wait for the rescue vehicle to get some medical equipment.

In any case, the life expectancy of the astronauts in such conditions is rather low and can be counted in tens of hours maximum.

Feedback and choice

Astronauts can reach the base only if they have the ability to move sufficiently, in the right direction and in the time allowed by their resources. Depending on their propensity to evaluate these dimensions, the astronauts will have to make a choice between two options:

• In general, the best option for the astronauts will be to stay at the landing site to take care of themselves and wait for the rescue vehicle. However, there are many situations where the vehicle is not able to reach the exact landing position or the time to get there is uncertain, or the reliability of the AI system is unsure. Numerous tests will have to be performed to assess the performance and robustness of that choice. • Try to reach the base or the vehicle. This is possible only if 0g effects have been mitigated, if the EVA-suit allows efficient walking and if the astronaut is in good shape.

In view of his central role, special attention must be paid to developing feedback on the three following elements:

Resources: Oxygen reserves, oxygen consumption rate, remaining time until loss of CO2 removal effectiveness, and battery lifetime, in particular. The interface of the suit may provide all needed information. In addition, part of the training must include the use of these systems and a simulation of an emergency situation.

Navigation system: Ideally a GPS-type tool can provide the astronaut with a map with geological cues, the position of the astronaut(s) as well as the directions and positions of the habitable module and the rescue vehicle(s). The position of the astronaut can be calculated by a satellite receiving a pulse signal emitted by a system attached to the spacesuit of the astronaut. Different options are possible. Several satellites can triangulate the position or a single satellite can infer the position by means of Doppler measurements (also used on Earth). However, several satellites must be orbiting at the same time to make sure that one of them is still present above while the others are behind the planet. Instead of a satellite, another space vehicle can be used. Remarkably, an areosynchronous orbit is proposed for the Earth return vehicle of several Mars mission architectures [START_REF] Salotti | Revised Scenario for Human Missions to Mars[END_REF][START_REF] Salotti | Robust, affordable, semi-direct Mars mission[END_REF]. This space vehicle cannot be used for accurate measurements as it would be too far from the planet. On the other hand, it could be the main vehicle for a communication relay to transfer information between the various players: the satellites, Mission control on Earth, the surface rescue vehicle(s), the astronaut(s) and maybe other assets on the surface. In case of communication problems or if the use of a satellite is not possible, the astronaut must pay attention to the last position of the landing module before triggering the ejection seat. Then an inertial unit attached to the ejection seat can provide complementary information about the final position on the surface. This information is very important as it can be used by the astronaut to determine his position. Nevertheless, the position is not sufficient, as the astronaut must be able to orient himself using a map and geological cues, the position of the sun (or stars by night). This is not an easy task. A dedicated system and a detailed procedure must be provided. Concerning the rescue vehicle, it must be ready to move by a simple command from the astronaut (through space communication relay). In case of communication problems, the command could come from Earth. Then artificial intelligence systems must be used on board the rescue vehicle to determine the best path to come as close as possible to the astronaut, taking obstacles into account. Once the signal from the vehicle can be detected by the astronaut's receiver, and vice versa, direction finding systems (based on the strength of the signal) can be used to determine the direction of movement with more accuracy [START_REF] Sklar | Modern HF Signal Detection and Direction Finding[END_REF].

The ability to move: This is a difficult dimension to quantify, and the astronaut is the one able to make this estimate. Refining this skill is one of the challenges of training, knowing that the context (gravity and fitness) during training will necessarily be different on Mars.

It is likely that the choice will be a luxury that the astronauts do not have if the base is too far away or if they cannot move after landing. However, if they have this possibility, it is important to provide a decision aid. Indeed, the astronauts' decision-making ability may be strongly affected by many factors (such as stress, pain and fatigue). Perhaps the software detailing the available resources can include this decision support. If the astronauts are able to establish contact with the base by radio, they may also find guidance and comfort. In this case, a detailed map of the landing area may be important to help the astronauts find their way around.

Rescue system for landing

It is proposed here to follow a similar final landing sequence to that of the Insight mission [START_REF] Clark | InSight tweaks trajectory to home in on Mars landing site[END_REF]:

• The ejection seat slows down under a disk gap band parachute.

• At one kilometre altitude (a dedicated sensor is used for real time measurements of the altitude), the velocity is around 60 m/s and it is the moment for parachute ejection and thruster ignition. Remark: As the seat can be ejected at lower altitudes, the velocity can be higher. The thrust has to be adapted to the situation. • Provided that there is still some time before impact, the velocity is decreased to reach 5 m/s at 30 metres above the surface. • The velocity is decreased to reach 1 m/s at 5 metres above the surface (it was 2.2 m/s for Insight).

• The velocity is kept constant until the surface is reached about 5 seconds later.

• Thrusters are turned off at touchdown. • Automatic rovers are sent to the landing site to rescue the astronauts.

Importantly, if the seat is ejected very late, the survival of the astronaut would depend on the maximum thrust of the engines and the human ability to support the load of the acceleration. In NASA reference missions, a 4G acceleration is mentioned as a maximum for the design of the EDL systems [START_REF] Drake | Mars Architecture Steering Group, Human Exploration of Mars[END_REF]. It is proposed here to use this constraint to determine the limits of the initial conditions to have enough time for slowing down before reaching the surface. Assuming a constant 4G deceleration using the thrust of the engines, the minimum altitude only depends on the initial falling velocity. This is defined by equation 1 and is plotted in Fig. 3. The horizontal velocity is not taken into account in the previous calculation. It is nevertheless considered in the maximum 4G tolerance. Let us assume that Mach 3 is the maximum viable velocity for triggering the ejection of the seat. Two cases have to be examined, with or without parachute:

𝐴𝑙𝑡 𝑚𝑖𝑛 = -0.5(𝑎 -𝐺 𝑚 )𝑡 2 + 𝑉 0 𝑡 (1)
• Without parachute, provided that the altitude is high enough, starting at 1020 m/s (Mach 3), the 4G deceleration would last 32 seconds to slow the vehicle down to 0. This duration can be used to determine the maximum amount of propellant required for the descent. Assuming a specific impulse of 230 seconds (based on the thruster used for the terminal descent of the Insight mission [31]) and a landing mass of 310 kg (see Table 3), the mass of propellant is given by equation 2 from Tsiolkovsky equation) and would be equal to 177 kg. • Using a parachute, the deceleration would not be linear. Let us assume that it would nevertheless be acceptable in the worst case scenario, at least until Mach 1 is reached (340 m/s). Then, using thrusters for the terminal braking phase, 50 kg of propellant would be enough if the thrust is optimized (equation 2), 60 kg with margins. As a parachute is a light device, the parachute option is therefore much lighter than the all-propulsive one.

𝑚 𝑝 = 𝑚 𝑓 (𝑒 ∆𝑣 𝑔 0 𝐼 𝑠𝑝 -1) (2)
With mp mass of propellant, mf final mass, Isp specific impulse and ΔV the velocity change requirement.

Total landed mass (w/o propellant)

As the mass is a critical parameter, the parachute option is proposed here. In order to minimise the risks of tilting at touchdown, the seat can be equipped with legs that would be deployed during the descent. The total mass of the rescue system -seat, parachute, thrusters and propellant -would be around 230 kg, about 370 kg with the astronaut and 310 kg for the landing mass. See Table 3 for a detailed budget mass and Fig. 4 for an estimation of the mass of the rescue system as a function of the mass of the spacesuit. Importantly, as a seat would be needed anyway, the additional mass for the DLS would be less, about 200 kg per Another mass penalty should nevertheless be taken into account for the ejection system and eventually for the reorganization of the architecture of the habitable module, which is not discussed here.

Probability risk assessment for a safe rescue using an autonomous vehicle

Let us consider that all astronauts safely land on the surface of Mars, what is the probability that they reach a safe haven in time? The main parameters are the autonomy of the spacesuit, the average walking speed, the distance to the base, the autonomy of the autonomous vehicle and its average speed, which depends on several other parameters such as the capacity of the engine, the type of terrain, the presence of obstacles and the performance of the automatic piloting system. Let us assume that the autonomy of the spacesuit is 8 hours and that the automated vehicle brings enough fuel and life support for a safe return.

An important question is the ability for the vehicles and the astronauts to cross obstacles. In general, however, the landing site is chosen in relatively flat regions, which reduces the risk of being blocked by obstacles. Regardless of possible insurmountable obstacles or accidents, the probability of reachability can be estimated. If the expectation of the average walking speed is v, the expectation of the maximum walking distance is 8v. A simple way to define a distribution function for that distance is to use a Gaussian distribution 𝑁 1 (8𝑣, 𝜎 1 2 ). In a similar way, if the expectation of the average speed for the autonomous vehicle is w, the expectation for the maximum distance after 8 hours is 8w and the Gaussian is 𝑁 2 (8𝑤, 𝜎 2

2 ). The total distance is given by a sum of Gaussians: 𝑁(8𝑣 + 8𝑤, 𝜎 1 2 + 𝜎 2 2 ). The probability of reachability is obtained by integration of the Gaussian (numeric method).

An important issue, however, is the lack of models for an estimation of the parameters of the Gaussians. While the average walking speed is speculative and depends on complex parameters, the standard deviation is linked to human variability. It is proposed here to look at marathon data [32]. Running a marathon and walking on Mars are very different activities, but the variability of the performance for the first activity, which can be expressed for example by a normalized standard deviation, provides an indication of the variability for the second. In 2010, for an average finishing time of 4 hours and 38 minutes, the standard deviation was 1 hour and 2 minutes, which represents 22.3% of the average speed. In this study, it is proposed to keep the same ratio to account for human variability. As regards the average speed of the vehicle, it strongly depends on the technical specifications that will be decided. For the Apollo mission, the lunar vehicle was able to reach 13km/h. In a recent study, it was suggested that 25 km/h would be an acceptable specification [START_REF] Baratta | Exploring the surface of the Moon or of Mars What kind of ground vehicles are required?[END_REF]. Though these speeds are relatively low, it is certainly possible to design faster vehicles if there are good reasons to do so. The greatest uncertainty comes from the terrain, which could be rough, rocky or sandy with the presence of obstacles. A comparable terrain, to a certain extent, has been encountered during the Dakar Rally, which occurred last year in the Arabic peninsula [START_REF]Dakar Rally Official Website[END_REF]. For that race, organizers tried to diversify the terrain, sometimes rocky, sometimes sandy, and potentially with unexpected obstacles that have to be skirted. The average speed of all stages was 110 km/h and the standard deviation was 16.4. In practice, the average speed and standard deviation values should be calculated according to the power of the vehicle and a detailed analysis of the landing site. For a first study, in order to take the variability of the terrain into account, it is proposed to use the Dakar standard deviation to average speed ratio, which is 14.9%. Based on these assumptions, the only unknown parameters of the Gaussians are the average walking speed and the average speed of vehicle. Two simulations are proposed with different values: a) Optimized: Assuming an efficient mitigation of 0g effects, an adaptation of the spacesuit for walking and a relatively fast vehicle, the average walking speed is around 3 km/h (walking at 4 km/h and making short stops) and the average speed of the vehicle is 20km/h. b) Pessimistic: It is assumed that the astronauts cannot walk and the vehicle has the same speed limit as the lunar rover of the Apollo mission (v=0km/h and w=13km/h). Results are presented Fig. 5 and6. The probability of reachability greatly depends on the capacity of the autonomous vehicle and on the type of terrain between the astronaut and the base. As the proposed risk analysis does not take accidents, insurmountable obstacles and other difficulties into account (e.g., communication problems), the probability of success is certainly lower. It does however provide a first insight into the risk. This result is interesting for two reasons -first, because in most situations, the landing site would not be that far from the base and secondly, the mass penalty for such a rescue system would be acceptable.

Conclusion

A rescue system has been proposed to reduce the risk of crew loss during the descent and landing phase of a human mission to Mars. It is based on an ejection seat for each astronaut, a parachute and a small propulsion system for the landing on the surface. For a successful rescue, the astronauts must wear a spacesuit with full life support and surface rovers must be present on the surface with automatic driving abilities to reach them, provide complementary life support and transport them back to the habitable module. Special attention must be paid to interface design and astronaut training so that the astronaut is able to evaluate the available options effectively.

Finally, the proposed study for the rescue on the surface after an emergency landing is linked with the more general problem of rescuing astronauts in operations on the surface. The problem has already been addressed by NASA and the recommendation was to constrain the EVA team to operate within rescue range of the outpost [START_REF] Hoffman | The Mars Surface Reference Mission: A Description of Human and Robotic Surface Activities[END_REF]. If there is a single pressurised and several unpressurised rovers, the rescue range is the maximum reachable distance of the vehicle with less capacity. In our study, however, the strongest constraint is not the distance, but the time to reach the astronaut and the capacity of automatic systems to drive vehicles in rough terrain with numerous obstacles. This capacity has to be analysed in detail for a better understanding of the risks.

Fig. 1 .

 1 Fig. 1. Vostok ejection seat (licence: Creative Commons).

Fig. 2 .

 2 Fig. 2. Ejection seat concept.

:Fig. 3 .

 3 Fig. 3. Minimum altitude for seat ejection (vertical axis in metres) as a function of initial falling velocity (horizontal axis in m/s).

Fig. 4 .

 4 Fig. 4. Mass of propellant and rescue system as a function of the spacesuit mass.

Fig. 5 .

 5 Fig. 5. Probability of reachability as a function of the total distance for case a) (optimized).

Fig. 6 .

 6 Fig. 6. Probability of reachability as a function of the total distance for case b).

Table 1 :

 1 Numerous missions failed during the descent to the Martian surface.

	Mars mission	Failure mode
	Mars 2	Parachute not deployed
	Mars 6	Contact lost during descent
	Mars 7	Retrorocket failure
	Mars polar lander Contact lost during descent
	Beagle 2	Contact lost during descent
	Schiaparelli	Wrong interpretation of sensors
		data during last phase of descent

Table 2 .

 2 Assessment of the type of vehicle.

		Automatic	Long distance range	Terrain	Weight	Life support
		deployment	(> 100 km)	adaptability
		on the surface
	Pressurised	Complex	Yes, but risky.	Average. Low in	Heavy	Yes, with
				mountains.		medical
						emergency
						capabilities
	Unpressurised Simple	Yes, provided that it is	Average. Low in	Light	No, or with
			equipped with a	mountains.		simple life
			deployable tent and			support (O2)
			life support systems.
			To be discussed.

Table 3 :

 3 Mass budget.

		Astronaut	80 kg
		Spacesuit, LSS included	60 kg
		Ejection seat (pyrotechnic	70 kg
		system not included)
		Parachute	20 kg
	Rescue system	Landing legs	10 kg
		Propulsion system (dry)	50 kg
		Propellant	60 kg
		Margins (10 %)	20 kg
		Total	230 kg


Large-Workspace Polyarticulated Micro-Structures Based-On Folded Silica for Tethered Nanorobotics Yuning Lei, Cédric Clévy, Jean-Yves Rauch, Philippe Lutz Abstract-Origami structures have a wide range of applications in robotics and have been intensively investigated by researchers in recent years. However, enabling sub-millimeter structures is an open question especially because of the lack of small enough joints. In this paper, compliant joints made of Silica by Focused Ion Beam (FIB) folding are proposed to achieve continuous, highly repeatable large motions. A polyarticulated structure including 3 joints is especially studied following a series of robotic analyses and experimentations to quantify the performances. The size of the structure firstly appears disruptive because smaller than 50 µm in typical overall length, i.e. less than the radius of an optical fiber. Secondly, the structure can achieve a planar workspace of 57 µm squared, which is significantly large compared to the structure dimension. Thirdly, repetitive movements performed at randomly selected positions, demonstrate an excellent repeatability standard deviations of 227 nm and 216 nm in x and y directions, respectively. These results together state the interest of novel polyarticulated structures resulting from the FIB folding as a basis for the next tethered nanorobotics generation.

Index Terms-Micro/Nano Robots, Actuation and Joint Mechanisms, Motion Control.

I. INTRODUCTION

A S a considerable amount of natural or artificially man- ufactured tiny objects such as cells, natural fibers [START_REF] Han | The role of microsporidian polar tube protein 4 (PTP4) in host cell infection[END_REF], carbon nanotubes [START_REF] Clevy | In-situ Versatile Characterization of Carbon NanoTubes using Nanorobotics[END_REF], and optical fibers have been increasingly used in recent decades for scientific, industrial and medical applications [START_REF] Bhushan | Springer Handbook of Nanotechnology, ser[END_REF]- [START_REF] Wang | Dynamic Modeling of Magnetic Helical Microrobots[END_REF], a strong need for characterization systems and methods to manipulate at very small dimensional scales has arisen. Some commercial systems, such as the Atomic Force Microscope (AFM) have allowed significant advances in this regard [START_REF] Pavlicek | Generation, manipulation and characterization of molecules by atomic force microscopy[END_REF], [START_REF] Shi | Recent advances in nanorobotic manipulation inside scanning electron microscopes[END_REF]. However, there are still substantial limitations due to the lack of dexterity and versatility in manipulation. That lead researchers to investigate another approach based on micro-and nanorobotics, The rapid development of micro-and nanoscale robotic devices [START_REF] Fatikow | Towards Robotbased Manipulation, Characterization and Automation at the Nanoscale[END_REF] in recent years has demonstrated the great potential of this approach.

To achieve multi-degree-of-freedom motion at the corresponding scale, the dimensions of the robotic system need to be as close as possible to the scale of the manipulation target to obtain sufficient manipulation dexterity. For nanorobotic applications, the size of their structures of interest is typically smaller than 100 µm [START_REF] Bhushan | Springer Handbook of Nanotechnology, ser[END_REF], [START_REF] Weir | A Review of Research in the Field of Nanorobotics[END_REF], [START_REF] Yao | A Review of Computer Microvision-Based Precision Motion Measurement: Principles, Characteristics, and Applications[END_REF]. Further research and development is needed to achieve more advanced micro structures with experimentally measured large workspace and high repeatability to verify their feasibility of application to nanorobotics. Since the physics and chemistry of this scale are not completely understood, such work is of considerable practical difficulty [START_REF] Fatikow | Towards Robotbased Manipulation, Characterization and Automation at the Nanoscale[END_REF], [START_REF] Weir | A Review of Research in the Field of Nanorobotics[END_REF]. In the past decades, various attempts have been made to achieve such ultra-small-scale dexterous motion, here we cite some state-of-the-art research in Fig. 1, among them, the miniaturization of origami structures is one of the aspects with great potential. Fig. 1. Comparison of the device size and approximate planar workspace of some representative active origami robots and micro structures developed in recent years. The devices in the area above the dotted line indicate that they have a large workspace compared to their size. Among them, large workspace sub-100 µm devices are in high demand for the development of nanorobotics [START_REF] Bhushan | Springer Handbook of Nanotechnology, ser[END_REF], [START_REF] Weir | A Review of Research in the Field of Nanorobotics[END_REF], [START_REF] Yao | A Review of Computer Microvision-Based Precision Motion Measurement: Principles, Characteristics, and Applications[END_REF].

Device Main Dimension

Origami-inspired folding techniques can convert a planar structure into a three-dimensional structure by folding, this feature makes origami well suited for improving the planarized structure design of conventional micro electro-mechanical systems (MEMS), the folds can be used as revolute articulations for robotic structure design. Some centimeter-scale origami structures have been proposed in recent years for robotic studies, for example, the milliDelta robot proposed by McClintock et al. [START_REF] Mcclintock | The milliDelta: A high-bandwidth, high-precision, millimeter-scale Delta robot[END_REF] and the multilayer deformable structure fabricated by Miyashita et al. [START_REF] Miyashita | Robotic metamorphosis by origami exoskeletons[END_REF]. Their design of robots with folding as structural articulations practically demonstrated the feasibility and guaranteed motion performance of this folding technology applied to polyarticulated robot design. The emergence of millimeter-scale micro origami structures has generated a great deal of interest, Leong et al. [START_REF] Leong | Tetherless thermobiochemically actuated microgrippers[END_REF] presented their untethered poly microgrippers with phalanges and joints, and Zhu et al. [START_REF] Zhu | Elastically and Plastically Foldable Electrothermal Micro-Origami for Controllable and Rapid Shape Morphing[END_REF] proposed bilayer-hinge-based sub-millimeter micro-origami structures to demonstrate the elastic and plastic deformation of folding, allowing the structure to undergo complex deformations, showing the great potential for further miniaturization of articulated origami structures.

Rauch et al. [START_REF] Rauch | Smallest microhouse in the world, assembled on the facet of an optical fiber by origami and welded in the µRobotex nanofactory[END_REF] fabricated the world's smallest origami house with a overall dimension of about 20 µm by applying a focused-ion-beam stress-induced deformation (FIB-SID) based self-folding process using a 1.2 µm thick silica membrane and a 1 µm thick lithium niobate membrane, respectively, on the cleaved surface of a single-mode fiber. The entire folding and assembly process was implemented in a SEM/FIB crossbeam vacuum station using a six-degree-of-freedom robotic manipulator. Their work has shown the feasibility of using rigid materials such as ceramics and silica, which are not traditionally collapsible, to create extremely small structures below 100 µm.

The work of Mao et al. [START_REF] Mao | Multi-Direction-Tunable Three-Dimensional Meta-Atoms for Reversible Switching between Midwave and Long-Wave Infrared Regimes[END_REF], [START_REF] Mao | Programmable bidirectional folding of metallic thin films for 3D chiral optical antennas[END_REF] demonstrates their method to control the angle of bi-directional folding of a 100 nm thick film between -70°and 90°by controlling the irradiation of a focused ion beam, which shows that the FIB-SID fabricated folding hinges have very small dimensions and a large angular range, and it is possible to obtain different hinges with similar thickness by controlling the folding to the same angle. From these works, we can see the prospect of designing and manufacturing more versatile polyarticulated robot structures.

However, the state-of-the-art research is still limited to the use of folds to form a specific angle in a passive origami structure, and there is no experimental evidence that such structures are capable of continuous motion within the angular range allowed by their mechanical strength, while the high repeatability required for nanomanipulations, typically less than 1 µm [START_REF] Fatikow | Towards Robotbased Manipulation, Characterization and Automation at the Nanoscale[END_REF], has not been verified in practice. To understand the suitability of such articulated structures for the development of nanorobotic applications, we still need to quantify the following aspect: Can such sub-100 µm articulated structures based on FIB-SID joints perform reversible, highly repeatable continuous motion over large workspaces?

To answer the question raised above, a sub-50 µm polyarticulated origami micro structure is introduced and studied in Section II, the structure is formed by cutting and self-folding a 900 nm thick fused silica membrane using a dual beam Scanning Electron Microscope (SEM)/Focused Ion Beam (FIB) station. The objective of this work is to investigate the angular range that each articulation of this FIB-SID polyarticulated origami structure can reach, so that the workspace of the structure's end-effector can be deduced through kinematic analysis in Section III and verified experimentally in terms of its workspace and repeatability, which are described in detail in Section IV and V respectively.

𝜃 3 y 0 x 0 y 2B x 2B y 3B x 3B y 1B y 1 x 1 x 1B y 2 x 2 FIB y x (2) 𝜃 2 y 0 x 0 y 1B y 1 x 1 x 1B y 2B x 2B y 3B x 3B

II. FOLDABLE MICRO-ORIGAMI STRUCTURES

Quite a few studies related to origami design and manufacturing method in SEM/FIB station, especially the self-folding origami process by Ga + ion implantation, have been made in recent years, various structures of different shapes have been proposed, such as micro-cubic structures [START_REF] Chalapat | Self-Organized Origami Structures via Ion-Induced Plastic Strain[END_REF], flowershaped and spiral structures [START_REF] Liu | Invited Article: Nano-kirigami metasurfaces by focused-ion-beam induced close-loop transformation[END_REF], [START_REF] Li | Focused-ion-beam-based nano-kirigami: from art to photonics[END_REF]. In this work, a possible way of investigating the robotic properties of sub-50 µm polyarticulated origami structures is provided by using a sixdegree-of-freedom closed-loop robot manipulator under the vacuum chamber of the SEM, with a centimetric workspace and nanometric accuracy. Details of the manufacturing and manipulation of the polyarticulated micro-origami structure are presented separately in the following subsections.

A. Manufacturing and folding of a polyarticulated microorigami structure

In this work, fused silica (silicon dioxide) has been used as a substrate membrane for cutting and folding the polyarticulated origami structure, and because it is a ceramic material and relatively easy to obtain homogeneous nanomembranes, its elastic behaviour is expected, which is important for the robotics, reversibility and repeatability of the robot's motions. Considering the technical difficulty of fabricating silica membranes below 1 µm in thickness, we set the thickness of the silica membrane to 900 nm to ensure that the resulting membranes have homogenous thickness and to reduce the risk of fracture. The complete fused silica membrane is obtained by wet etching the oxidized silicon wafers with HF and KOH solutions.

As single folds have been demonstrated as feasible in previous research [START_REF] Rauch | Smallest microhouse in the world, assembled on the facet of an optical fiber by origami and welded in the µRobotex nanofactory[END_REF], [START_REF] Mao | Programmable bidirectional folding of metallic thin films for 3D chiral optical antennas[END_REF], We desired a structure with at least three revolute articulations and which could work in the 2D plane to enable the characterisation of motion in SEM view. Fig. 2 demonstrates the design and fabrication process of the polyarticulated origami structure chosen as case study for the purpose of the objective of the study. A sub-50 µm long cantilever is designed to perform the FIB-induced folding and a triangular tip is created at the end-effector location for ease of subsequent measurements using computer vision methods. A small segment is designed to be cut and folded from the middle of the cantilever for welding with the stretched fiber tip. The thickness of the folded hinges has been measured to be approximately 100 nm, hence, to ensure that they do not break during movement, the minimum segment width is set around 8 µm to ensure the robustness of each hinge for repeatable folding, resulting in a width of 15 µm for the entire cantilever. The length of the structure was limited to 50 µm in order to comply with the target size requirements.

TABLE I PARAMETERS OF THE ORIGAMI PROCESS FOR DIFFERENT SEGMENTS

Segment Etching zone

Step 1: Trimming

Step 2: Folding Consequently, a 45 µm × 15 µm pattern with a triangular tip and a fixed end on the other side is cut on the fused silica membrane by the focused ion beam, shaping the body of the structure, a 6 µm × 8 µm small segment a 3 was being cut and folded firstly from the part near the triangular tip. After this, the structure was divided into two segments of a 1 = 20 µm and a 2 = 25 µm in length and folded them in turn. The origami folding process of each segment was divided into two steps, with the first step using a stronger ion current to trim the silica membrane into thin hinges, followed by a weaker ion current to achieve a better control of the folding angle of each segment. The joint deformation limits of these hinges can be varied by changing their width h 1 , h 2 and h 3 , in our experiments, they were all set to 1.3 µm to ensure a consistent angular range for each articulation. The FIB parameters of these origami folding process are described in Table I for all three segments. The final angle of each articulation during the folding process needs to be set to a similar value of less than 90 degrees to ensure that the thickness of the flexible hinge is approximately the same and that they will not interfere with the subsequent folding of the other segments by obstructing the focused ion beam. B. Activating the polyarticulated micro-origami structure using a stretched optical fiber tip

The handling and deformation of the polyarticulated microorigami structure is controlled by a six-degree-of-freedom (6-DoF) robotic manipulator, which is composed by SmarArt actuators in the vacuum chamber of the SEM. An optical fiber tip end with a stretched diameter of 1 µm is mounted on the end-effector of the robot to activate the polyarticulated microorigami structure, as shown in Fig. 3.

The two free ends of the second and third segment are called point A and point B, respectively, corresponding to the output motion and the input motion end, shown in Fig. 2 b(3). In the experiment, the tip of the fiber was manipulated to contact point B on the third segment of the polyarticulated structure, and a Gas Injection System (GIS) was used to perform Ion Beam Induced carbon Deposition (IBID), carbon were deposited to weld the tip of the fiber to the third segment of the structure for reinforcement.

III. MODELING

In this section, the kinematic model of the proposed polyarticulated structure is presented in detail, demonstrating the relationship between the angle of each fold of the polyarticulated structure and the position of the end-effector obtained by using kinematic solutions. Each fold in the polyarticulated structure is regarded as a revolute joint for this purpose. This model is thereby used to simulate its workspace in the measured joint limits.

Following the definition of commonly used Denavit -Hartenberg (D-H) convention, the fixed link frame is defined as {x 0 , y 0 , z 0 }, and the coordinate frame of Link i is defined as {x i , y i , z i }. The standard Denavit-Hartenberg (D-H) parameters of the polyarticulated origami structure considering the point A as end-effector are presented in Table II and the D-H coordinate system is detailed in red notations in Fig. 2

(b)(1-2).

Considering the polyarticulated structure as a two-degreeof-freedom (2-DoF) planar serial chain with two revolute joints (RR), the kinematics equation 0 T 2 for the series chain of output motion point A can be obtained by using the lengths and angles of the three segments that make up the polyarticulated structure:

0 T 2 = 0 T 1 • 1 T 2 (1)
Therefore, the transformation matrix of the end-effector A can be described as follows:

0 T 2 =     c 12 -s 12 0 a 2 c 12 + a 1 c 1 s 12 c 12 0 a 2 s 12 + a 1 s 1 0 0 1 0 0 0 0 1     (2) =     c φ A -s φ A 0 x A s φ A c φ A 0 y A 0 0 1 0 0 0 0 1     (3)
Here we note c i = cos (θ i ), s i = sin (θ i ), c ij = cos (θ i + θ j ), s ij = sin (θ i + θ j ) . So the output forward kinematic solution of the end-effector A can be obtained:

   x A = a 2 c 12 + a 1 c 1 y A = a 2 s 12 + a 1 s 1 φ A = θ 1 + θ 2 (4)
• ≤ θ 1 , θ 2 ≤ 60 • , (b) -90 • ≤ θ 1 , θ 2 ≤ 90 • , (c) -120 • ≤ θ 1 , θ 2 ≤ 120 • , (d) -150 • ≤ θ 1 , θ 2 ≤ 150 • .
From these equations, the angular values can be used to get to the position of the point A by applying this forward kinematics solution. Based on the limitations of each flexible hinge, the workspace of the point A was also calculated, as shown in Fig. 4. The Robotic Toolbox [START_REF] Corke | Robotics, Vision and Control, ser. Springer Tracts in Advanced Robotics[END_REF] in Matlab was used to model a two-axis planar robot with the parameters in Table II. When using the analytical method [START_REF] Yanjiang | A Method for Solving Robot Workspace Based on Matlab[END_REF], [START_REF] Li | Analysis of robotic workspace based on Monte Carlo method and the posture matrix[END_REF] to calculate the workspace, different resulting areas were obtained with positive or negative θ 2 values respectively, with a partial area overlapped between them.

The angle of each revolute joint can be obtained by solving the inverse kinematic model (IKM) for the input motion of the point B, and thus the position of the end-effector A can be obtained using the forward kinematic model (FKM).

  x B y B φ B   IKM ---→   θ 1 θ 2 θ 3   F KM ----→   x A y A φ A   (5)
The D-H coordinate system parameters considering the point B as end-effector are presented in Table III and detailed in yellow notations in Fig. 2(b)(1-2). Especially, in order to distinguish with the coordinate system of point A, we define {x iB , y iB , z iB } as the Link i frame of the D-H coordinate system of point B. Therefore the inverse kinematic solution can be obtained for point B using the iterative algorithm provided in the Robotic Toolbox.

According to the simulation results in Fig. 4, we can expect the structure proposed in section II to have a workspace of the same order of magnitude as the structure itself. This workspace depends very largely on the amplitude of each joint, the limits of the joints will be studied in the next section. IV. EXPERIMENTAL EVALUATION this section, the attainable angle of articulation is quantified firstly in order to adapt the workspace of the polyarticulated origami structure obtained from the simulation to the actual joint limits, then the experimental procedure is described and the workspace is quantified experimentally to verify that the workspace obtained from the kinematic model is practically attainable.

for positive for negative Fig. 6. Validation of the workspace of the polyarticulated origami structure: Simulation of the workspace of the validated joint confinement range (solid line) with the coordinates of the end-effector point A (red star marks) obtained from experimental measurements. The shaded part of the workspace cannot be verified due to the occlusion of the substrate

A. Quantification of joint angle range

By means of machine vision-based image correlation, the image pixel coordinates of the vertices of each rigid segment are measured and converted to coordinates in the work plane of the polyarticulated origami structure according to the pixel size. The placement of the sample has been adjusted so that the work plane of the structure is as perpendicular as possible to the direction of the scanning electron beam, making it easier to perform measurements and coordinate system conversions.

The positions of each rigid segment endpoint are measured and calculated using the cosine rule to obtain the angle values as shown in Equation 6, refer to Fig. 2(b3), the sign of the result depends on whether the angle is folded forwards or backwards.

θ 1 = ± cos -1 OD 2 + OE 2 -DE 2 2 × OD × OE θ 2 = ± 2π -cos -1 AD 2 + OD 2 -AO 2 2 × AD × OD θ 3 = ± cos -1 AC 2 + BC 2 -AB 2 2 × AC × BC (6)
In the experiments, the maximum folding limit angle of each flexible hinge was measured to be 0 ≤ θ 1 ≤ 152.3 • , -101.6 • ≤ θ 2 ≤ 151.7 • , distributions of the measurements of the joint angles are shown in Fig. 5. Due to the obstruction of the field of view by the fused silica membrane, in practice, only the configuration of θ 1 folding in the forward direction can be experimentally observed, so we use these measurement results as the joint range for this structure for the workspace analysis of the point A, hence the workspace calculated using these parameters is shown as solid envelope lines in Fig. 6.

B. Validation of the workspace

The polyarticulated structure was activated to move with each joint varied in its measured joint range, a sequence of movements was obtained to validate the calculated workspace. Each motion step was performed with a movement of a few micrometers, and a set of images of the SEM view was saved for position measurement. Due to the limitations of the rotation angle, once the optical fiber tip is welded to the polyarticulated structure, the optical fiber tip was controlled to move only in the x and y directions without any rotation, therefore the entire workspace needs to be separated in two zones: the one with a positive θ 2 and the other with a negative θ 2 . In these two cases, the welding direction of the fibers is different, so these two cases were experimented separately. The part of the workspace below the silica membrane could not be experimentally observed and verified due to the obstruction of the field of view by the membrane, Thus only the workspace above the membrane has been experimentally verified.

In Fig. 7 images are shown with θ 2 folds in positive direction, and another case with θ 2 folds in the opposite direction is represented on the right side of Fig. 7 (e-h). These images are used to characterize the joint angles and analysis the position of endeffector A.

The workspace of the end-effector A was verified by placing the measured points in the structure coordinate system as red marks in Fig. 6. The shaded area cannot be verified because it was shielded by the fused silica membrane and silicon substrate. The workspace achievable by the proposed polyarticulated micro-origami structure within the determined angular constraints was measured to be 57 micrometers squared, of which we verified a workspace of approximately 47.4 micrometers squared with experimental data.

V. EXPERIMENTAL REPEATABILITY STUDY

The repetitive movement experiences of determined poses performed by the proposed polyarticulated micro-origami structure are presented in this section to analyse the repeatability and reversibility of motions generation in nanoscale.

The joint parameters of the six-degree-of-freedom robot for a defined position in the workspace of the micro-origami structure were recorded, and twenty repetitive motions were made to this configuration, with sampling the end-effector position five times for each move to the saved position to reduce measurement uncertainty. Since the transformation between the discrete image coordinates system R i (u, v) in pixels and the robot workspace nanometric coordinates system R r (x, y) is calculated by Equation 7, The homogeneous coordinates of the end-effector A in the image coordinate system and the robot coordinate system are expressed respectively as (u A , v A , 1) and (x A , y A , 1), the image coordinates of the endeffector A were measured by the same vision-based method as being described in the previous section and obtain the point coordinates distribution within the robot's workspace by multiplying the coordinates by the size of each pixel (k x , k y ) in the image.

  x A y A 1   =   k x 0 0 0 k y 0 0 0 0   •   u A v A 1   • i T r (7)
Here i T r is the transformation matrice from image coordinate system to the polyarticulated origami workspace coordinate system, R r (x, y) corresponding the one in Fig. 2 b,k x and k y are the image nanometric pixel size in lateral and vertical directions.

The results of the measurements are shown in Fig. 8. The positioning repeatability is defined by its standard deviation of all repeated positions to the mean position, in lateral, std x , and in vertical, std y .

x = 1 n n j=1 x j , ȳ = 1 n n j=1 y j (8)
std x = n j=1 (x j -x) 2 n -1 , std y = n j=1 (y j -ȳ) 2 n -1 (9)
The experimental result shows that these repetitions follow a normal distribution of 227 nm and 216 nm standard deviation along x and y directions, respectively, for displacements of 20 µm. Due to limitations in image resolution and the effect of image distortion caused by the scanning electron beam, the five measurements of each single pose have an average error of 183 nm, which is in the same order of magnitude as the experimental results. Accordingly, we can conclude that the intrinsic repeatability is limited by the conditions of measurement, the actual motion repeatability of the structure can be much better than the obtained experimental results.

VI. CONCLUSION

In this article, we presented a sub-50 µm polyarticulated micro-origami structure made of a 900 nm thick fused silica membrane fabricated using FIB-induced folding process. The work demonstrated that this folded structure can induce reversible motions and thus the folded hinges can be considered as articulation. Every articulation can achieve a reversible large angle range between -101.6 and 152.3 degrees, and the polyarticulated structure is therefore able to reach a very large workspace of 57 µm squared, and it has been verified that 47.4 µm squared of this workspace is safe and experimentally achievable. The device size to workspace ratio was demonstrated at the same scale and makes it compatible with the considerable demand domains for large workspace nanorobotics devices smaller than 50 micrometers. Proposed polyarticulated structure enables reversible motions with a repeatability standard variance experimentally measured as 227 nm and 216 nm along the x and y directions, respectively, which demonstrates that this polyarticulated structure is suitable for motions and operations in nanorobotics, and thus provides the basis for subsequent design and fabrication of more dexterous sub-100 µm parallel robotic structures based on FIB-induced folding articulations, such as self-adaptive robotic fingers [START_REF] Birglen | Type synthesis of linkage-driven self-adaptive fingers[END_REF], for the next tethered nanorobotics generation.

ACKNOWLEDGMENT

This work was supported by the Equipex ROBOTEX (ANR-10-EQPX-44-01), the COLAMIR Project (contract ANR-19-CE10-0004-01), Région Bourgogne Franche-Comté, the EIPHI Graduate School (ANR-17-EURE-0002) and the French RENATECH network through its MIMENTO technological facility. The authors are also very grateful to Pierre Roux, Laurent Robert, Marion Vieira and Joël Agnus for their contribution in the design and fabrication of the wafers and experimental setup.

Fig. 2 .

 2 Fig. 2. (a) Planar Design of the micro-origami structure before folding. (b) The folding process of the origami: folding of each of the three rigid segments of the structure (1-3). schematic illustrations of side view, along with top view (FIB images), Scale bars are 10 µm. The two free ends of the second and third segment are called point A and point B, respectively, and C, D and O represent the articulations between segments. We define E as a certain point along the x-axis for subsequent joint measurement and algebraic representation. The Denavit-Hartenberg (D-H) coordinate system of A and B are shown in red and yellow notations respectively in (1-2). (c) (1-2) Side view SEM images of the polyarticulated micro-origami structure after cutting and folding process completed. (3) Demonstrate the thickness of the silica membrane and of the folded hinges, measured as 925 nm and 104 nm respectively.

Fig. 3 .

 3 Fig. 3. Experimental configuration for welding and activating the polyarticulated origami structures with a stretched optical fiber tip. The locally zoomed-in rendering at the bottom left shows the micro origami structure folded on the silica membrane.

Fig. 4 .

 4 Fig. 4. Workspace simulation results obtained using analytical method, for different joint limits of θ 1 and θ 2 . (a) -60• ≤ θ 1 , θ 2 ≤ 60 • , (b) -90 • ≤ θ 1 , θ 2 ≤ 90 • , (c) -120 • ≤ θ 1 , θ 2 ≤ 120 • , (d) -150 • ≤ θ 1 , θ 2 ≤ 150 • .

Fig. 7 .

 7 Fig. 7. Proof of concept of folding and actuation of the polyarticulated structure by the externally driven optical fiber. (a1)-(d1) Schematic representation of the changes of the joints during movement with θ 2 folding in positive direction and (e1)-(h1) in negative direction. (a2)-(d2) Example of the SEM images obtained from the experiment for measuring and calculating the values of the angles and determining the position of the end-effector using visual methods, (e2)-(h2) are in negative direction. The arrows in the SEM images represent the direction of motion of point A (red) and point B (yellow) respectively. Scale bar is 5 µm for all images.

Fig. 8 .

 8 Fig. 8. Repeatability test, distribution of the results of 100 measurements for 20 repetitions of the determined pose (5 measurements per pose), The size of bubble indicates the density of the data measured at that point.

  Joint angle Link offset Link length Link twist

			TABLE II
	STANDARD DENAVIT-HARTENBERG PARAMETERS OF ORIGAMI
	STRUCTURE WITH POINT A CONSIDERD AS END-EFFECTOR
	Link	θ i	d i	a i	α i

TABLE III STANDARD

 III DENAVIT-HARTENBERG PARAMETERS OF ORIGAMI STRUCTURE WITH POINT B CONSIDERD AS END-EFFECTOR

	Link	θ i Joint angle Link offset Link length Link twist d i a i α i
	1	θ 1	0	a 1	0
	2	θ 2	0	a 4	0
	3	θ 3	0	a 3	0
	Fig. 5. Distribution of experimentally measured joint angle values of θ 1 and
	θ 2 , The maximum joint angle obtained is 152.3°and the minimum joint angle
	is -101.6°.

This paper was recommended for publication by Editor X. Liu upon evaluation of the Associate Editor and Reviewers' comments. This work was supported by ISITE-BFC (contract ANR-15-IDEX-03), Equipex ROBOTEX (ANR-10-EQPX-44-01), ANR (ANR-19-CE10-0004-01), by Région Bourgogne Franche-Comté and the EIPHI Graduate School (ANR-17-EURE-0002).