Lavindra De

Silva Amit

Kumar Pandey
email: akpandey@laas.fr

Mamoun Gharbi
email: magharbi@laas.fr

Rachid Alami
email: rachid@laas.fr

Towards Combining HTN Planning and Geometric Task Planning

In this paper we present an interface between a symbolic planner and a geometric task planner, which is different to a standard trajectory planner in that the former is able to perform geometric reasoning on abstract entities-tasks. We believe that this approach facilitates a more principled interface to symbolic planning, while also leaving more room for the geometric planner to make independent decisions. We show how the two planners could be interfaced, and how their planning and backtracking could be interleaved. We also provide insights for a methodology for using the combined system, and experimental results to use as a benchmark with future extensions to both the combined system, as well as to the geometric task planner.

I. INTRODUCTION

The past few years have seen a great deal of interest in interfacing symbolic and geometric reasoning. A common theme has been to define how geometric entities and capabilities should be meaningfully used within symbolic planning, and how symbolic information can be used, perhaps as heuristics, in geometric planning. In this paper we follow this trend. Broadly, we are interested in the link between a geometric task/action and a symbolic action, what geometric information we should publicise to the symbolic (resp. geometric) planner, and how can we include them in symbolic (resp. geometric) states and actions. An unavoidable issue that arises when combining the two planning approaches is "backtracking"trying alternative options for choices that were already made during planning. Both approaches are capable of backtracking at their own levels when a plan being pursued turns out to not work: the symbolic planner when some precondition is not met, and the geometric planner when a path/trajectory being planned cannot avoid a collision. It is therefore important to decide how we can effectively interleave geometric and symbolic backtracking [START_REF] Pandey | Mightability maps: A perceptual level decisional framework for co-operative and competitive human-robot interaction[END_REF], [START_REF] Karlsson | Combining task and path planning for a humanoid twoarm robotic system[END_REF], and how we should switch between them.

In [START_REF] Karlsson | Combining task and path planning for a humanoid twoarm robotic system[END_REF], [START_REF] Lagriffoul | Constraint propagation on interval bounds for dealing with geometric backtracking[END_REF] the authors discuss algorithms for geometric backtracking by extending the Justin robot with symbolicgeometric planning capabilities: they use the JSHOP2 [START_REF] Nau | Total-order planning with partially ordered subtasks[END_REF] HTN planner for the symbolic planning component and a specialised path planner for the geometric one. Unlike our approach, the authors keep the symbolic state orthogonal to the geometric state: changing, for instance, the pose of an object on a table has no consequence on the symbolic state. We require symbolic and geometric states to be intertwined, which is natural in some domains. To this end, we derive symbolic facts from the geometric state and use these in symbolic planning.

To interface symbolic and geometric planning, the authors in [START_REF] Dornhege | Integrating symbolic and geometric planning for mobile manipulation[END_REF], [START_REF] Dornhege | Semantic attachments for domain-independent planning systems[END_REF] introduce "semantic attachments," which associate selected predicates in the planning domain to external procedures called at runtime to evaluate the predicates. In [START_REF] Dornhege | Integrating task and motion planning using semantic attachments[END_REF], the semantic attachments are implemented using a trajectory planner that computes collision free trajectories; if one exists, then the corresponding semantic attachment evaluates to true, and false otherwise. Likewise, we use "evaluable predicates," with a minor difference where we link them to more abstract entities called geometric tasks, which may or may not invoke a trajectory planner. The authors also introduce "effect applicators" in effects of actions that consult the geometric planner to set certain state variables (e.g. position and orientation of a moved object) in the symbolic domain. Effect applicators, however, cannot make decisions between different outcomes, such as choosing where to place an object. In our work we do want to give the geometric planner some leeway to make such choices.

In some works there is a tight integration between symbolic and geometric planning. In [START_REF] Wolfe | Combined task and motion planning for mobile manipulation[END_REF], for instance, a hierarchical planner plans all the way down to the level of geometric actions. Similarly, [START_REF] Kaelbling | Hierarchical task and motion planning in the now[END_REF] describes a special purpose hierarchical planner combined with a geometric motion planner for planning, and then executing the most basic actions while the plan is still being constructed. This is different to the work described above which formulate a complete plan first, before executing it. The Asymov [START_REF] Cambon | A robot task planner that merges symbolic and geometric reasoning[END_REF] system is a combined task and motion planner for problems that are difficult to solve when the symbolic planner is in control of the geometric search, e.g. in the geometric Towers of Hanoi problem that the authors present. Compared to other approaches, in Asymov the geometric planner uses the symbolic planner-as well as the symblic model of the domain-as a heuristic when choosing roadmaps during geometric search. Similarly, in [START_REF] Plaku | Sampling-based motion and symbolic action planning with geometric and differential constraints[END_REF] a symbolic planner guides a sampling-based motion planner, which in turn sends back utility estimates to improve the guide in the next iteration.

Unlike previous approaches, our work concerns the use of a geometric task planner instead of a typical trajectory planner; the former lets us define the interface to symbolic planning in a more meaningful way-by providing a higher level of abstraction to low level geometric actions like picking and placing-and also gives more leeway to the geometric level to make decisions. Unlike past work we are also interested here in a principled methodology for developing symbolic-geometric planning domains: this paper provides useful insights in this direction. We present an initial prototype implementation of the combined planning framework including basic interleaved backtracking, and an analysis of its runtime performance; we intend to use these results as a benchmark for future experiments with different backtracking strategies currently being developed, and to develop better heuristics for the geometric task planning component itself.

II. BACKGROUND

In this paper we refer to the popular STRIPS classical planning language [START_REF] Fikes | STRIPS: A new approach to the application of theorem proving to problem solving[END_REF]. More importantly, we make use of the Hierarchical Task Network (HTN) planning formalism. While classical planners focus on bringing about states of affairs or "goals-to-be," HTN planners focus on solving abstract tasks or "goals-to-do." In this paper we use a popular type of HTN planning called "totally-ordered" HTN (henceforth simply referred to as HTN) planning, which has proven to be efficient in certain domains [START_REF] Nau | SHOP: Simple hierarchical ordered planner[END_REF]. An HTN planning problem is the 3-tuple d, S 0 , D, where d is the sequence of (primitive or abstract) tasks to solve, S 0 is an initial state as in classical planning, and D is an HTN planning domain. Specifically, an HTN planning domain is the pair D = A, M where A-the primitives of the domain-is a finite set of operators as before, and M is a finite set of methods. A method is a tuple consisting of the name of the method, the abstract task that the method is used to solve, a precondition specifying when the method is applicable (like an operator's precondition), and a body indicating which tasks are used to solve the task associated with the method. The method-body is a sequence of primitive and/or abstract tasks. The planning process works by selecting applicable reduction methods from M and applying them to abstract tasks in d in a depth-first manner. In each iteration this will typically result in d becoming a "more primitive" sequence of tasks. The process continues until d has only primitive tasks left. At any stage in the planning process, if no applicable method can be found for an abstract task, the planner essentially "backtracks" and tries an alternative method for an abstract task refined earlier.

For the geometric counterpart, we adopt the approach of finding a solution in a discrete space of candidate grasps and placements [START_REF] Lagriffoul | Constraint propagation on interval bounds for dealing with geometric backtracking[END_REF], [START_REF] Pandey | Towards planning human-robot interactive manipulation tasks: Task dependent and human oriented autonomous selection of grasp and placement[END_REF] for tasks involving picking and placing. Basically, our geometric task planner (GTP) 1 iterates in a four dimensional search space, consisting of a set of agent "effort" levels, a set of discrete grasps, a set of object placement positions, and a set of object placement orientations (see Figure 1). For each object, sets of possible grasps are pre-computed and stored for the anthropomorphic hands and the robot's gripper, which are later filtered based on task requirements and the environment. The amount of "effort units" required to perform certain tasks like moving the head, extending an arm, and standing up are predefined; to this end, we have made simplifying assumptions about which tasks (e.g. head movements) require less effort than others (e.g. standing up). At runtime, sets of placement positions and possible orientations of objects are dynamically extracted, based on the environment, the task, and restrictions on how much effort should be put into the task. These sets are then weighted based on the environment and situation, with criteria such as grasp and placement stability, feasibility of simultaneous grasps by two agents, the agent's visibility of the object, and estimated effort to see and reach it.

The advantage of the GTP framework is that a variety of day-to-day tasks like showing, giving, hiding, and making accessible can be represented in terms of different constraints, based on factors like reachability, visibility, desired effort level, and the ability to grasp. A geometric solution is found using a constraint hierarchy based approach, by carefully introducing these constraints successively at different stages of planning. This facilitates the reduction of the search space successively, before introducing relatively more computationally expensive constraints.

We shall now briefly highlight the GTP algorithm. The outermost loop starts from the lowest estimated effort required (to view and reach objects) for the task and incrementally moves to the highest. For each such effort estimate, the algorithm iterates on the candidate points where the task could be performed, excluding those that did not work with lower effort estimates. For each such point, the algorithm iterates on the possible object grasps if it is not already in the gripper, excluding those that already failed for lower effort estimates. For each such grasp, if a collision-free pick is possible-i.e. there is a path to a configuration associated with the graspthe algorithm tries the different possible object orientations, excluding those that are in collision (e.g. with a surface), and those that do not satisfy the visibility threshold and other task oriented symbolic constraints, such as maintaining the object facing front. Finally, the planner obtains a tuple consisting of a grasp, a placement position and a placement orientation, which is then used to find a collision free trajectory.

III. A SYMBOLIC-GEOMETRIC PLANNING EXAMPLE

In this section we detail a concrete domain that illustrates how symbolic and geometric planning is interfaced and combined. We also highlight our approach to interleaving HTN and GTP backtracking, but leave the detailed algorithms for a separate paper. Suppose a PR2 robot is working as a library receptionist. Library members reserve books online with their membership ID, which is also used to top up their library credit. The ID can be used to look up membership details like email address and books reserved and borrowed. Reserved books are collected in person from the library. Once an online reservation is made, (human) librarians make the books accessible (i.e. reachable without navigating from the current position, and visible) to the PR2 on an adjacent table. Fig. 2: The part of the HTN domain that handles online book reservations. Solid rectangles are HTN abstract tasks, rounded rectangles are methods (where the incoming vertex is the task that the method solves, and outgoing vertices are the tasks in the method's body), and dashed rectangles are actions. Standard HTN actions are in bold and GS actions are underlined. The HTN domain is illustrated graphically in Figure 2 and detailed in Table I. The top-level HTN task is MANAGEORDER(M ) for member M . It has one method (named m 1 ) with two subtasks: LEND(M ) and TAKEPAYMENT(M ). The first is associated with three methods-m 2 , m 3 , m 4 -which are tried in that order. Method m 2 trivially succeeds if there are no (more) books held by the member and hence no more books to give. If it is not applicable, m 3 is tried, which has the following actions: pick (via GTP) from the adjacent shelf a book reserved by the member, speak out the title, make it accessible to the member on the desk, perform some bookkeeping-e.g. send the current total to the Point-of-Sale (POS) machine-and then recursively call LEND(M ).

ACTION/HTN TASK M PRECONDITION METHOD-BODY/ACTION-EFFECTS MANAGEORDER(M ) m1 held(B, M ) LEND(M ) • TAKEPAYMENT(M ) LEND(M ) m2 ∀B, ¬held(B, M ) m3 held(B, M ) ∧ title(B, T ) PICK(B) • SAY(T ) • MAKEBKACC(B, M ) • ADD(B, M ) • LEND(M ) m4 held(B, M ) ∧ title(B, T ) ∧ ¬hvy(B) DISPLAY(B, T, M ) • GIVEBK(B, M ) • WAITTAKE(B, M ) • ADD(B, M ) • LEND(M ) DISPLAY(B, T, M ) m5 true PICK(B) • SHOW(B, M ) • SAY(T ) TAKEPAYMENT(M ) m6 numLent(M, N ) DEBITACC(M, N * cost) m7 numLent(M, N ) ∧ cred(M, C) ∧ (C < N * cost) PLACEPOSM() • PUTAWAYPOSM(M ) • EMAIL(M ) PLACEPOSM() m8 reachable(mac, pr2) PICK(mac) • SAY(swipe) • PUTON(mac, stnd) m9 true NAVTO(mac) • PICK(mac) • NAVTO(desk) • SAY(swipe) • PUTON(mac, stnd) PUTAWAYPOSM(M ) m10 true SAY(thank) • PICK(mac) • PUTAWAY(mac, M ) SAY(T ) true {spoke(T )} MAKEBKACC(B, M ) held(B,
Method m 4 starts with an HTN abstract task to display a book, which refines into the three steps focussed on showing a book to the person. The abstract task is followed by giving the book to the person, 2 waiting for it to be taken-which relies on the gripper angle and force sensors to check if the book has successfully been taken-and then the bookkeeping action as before, ending with a recursive call to LEND(M ). Note that a book is given only if it is deemed light enough to be directly taken from the gripper, and that by forcing an ordering on m 3 and m 4 we are encoding a preference for placing a book on the table over handing it (directly) to the member, allowing the member to pick up the book and put it in a bag/handbag at his/her own pace.

The TAKEPAYMENT(M ) task of m 1 has methods m 6 and m 7 . Method m 6 has a single action to debit the account corresponding to the member ID according to the number of books lent (all books have the same cost), if there is enough credit C in the member's account. If not, the member must pay by credit card (m 7 ). The PLACEPOSM(M ) task refines into two methods for giving the POS machine: if the machine is (likely) reachable it is simply picked up, but if notpresumably because the (shared) machine is with the receptionist at an adjacent desk-the PR2 navigates to the machine, picks it up, and navigates back; the PR2 then asks the user to swipe the card and enter the PIN, and then puts the machine on the POS machine stand. The PUTAWAYPOSM(M ) task includes actions to thank the person and to put the machine somewhere that is away from the person's reach and visibility, and EMAIL(M ) emails the member an invoice.

This HTN domain serves to highlight some key features. First, the HTN developer interfaces with the GTP using evaluable predicates. To this end, every (relevant) GTP task t is associated with an evaluable predicate-denoted t ? -in the HTN domain (e.g. GTP task SHOW(O, H) has evaluable predicate show(O, H) ? for some object O and human H), which evaluates to true if t has a GTP solution and false otherwise. Whenever such an evaluable predicate is mentioned in the precondition of an operator (resp. action), we call it a Geometric-Symbolic (GS) operator (resp. action). A GTP task t is also associated with an add list function-denoted t + -and a delete list function-denoted t --which are the (possibly empty) add and delete lists for t computed by the GTP, based basically on the world resulting from the solution that was found for t on calling evaluable predicate t ? . Add list function show(o 1 , h 1 ) + might, for instance, return the set {visible(o 1 , h 1 ), accessible(o 1 , h 1 )} and show(o 1 , h 1 ) -the set {visible(o 3 , h 1 ), accessible(o 3 , h 1 )}: that is, after making object o 1 visible to human h 1 , the object is also accessible to h 1 , but object o 3 is no longer visible nor accessible to h 1 . The effects of a GS operator is the combination of its "static" add and delete lists with those obtained via the add and delete list functions.

An important concept we exploit is that of a "shared predicate" (or "shared literal"), which is a standard literal that is based on geometrical properties and hence modelled more accurately by the GTP. For example, predicate reachable(o, h) in the HTN domain (see method m 8 ), which specifies that object o is reachable to human h, is derived from the 3D world with a heuristic based on the area covered on extending the robot's arm with respect to all its degrees of freedom [START_REF] Pandey | Mightability maps: A perceptual level decisional framework for co-operative and competitive human-robot interaction[END_REF].

We highlight some interesting interleaving of GTP and HTN planning-backtracking in particular-possible with the domain described. Suppose the library reception desk is small and somewhat cluttered, and that a member has reserved two big books b 1 and b 2 . Assume there is enough space on the table to make one of them accessible (to the member), but not enough space to make them both accessible, nor to make one accessible but give the other (directly), as the books are so big that they block the robot-arm's path to the person. Figure 3 shows a part of a possible combined HTN-GTP planning scenario. In the figure, b 1 is successfully picked and made accessible-i.e. the GTP tasks (third column) corresponding to the PICK(b 1 ) and MAKEBKACC(b 1 , m) GS actions (second column) are successfully planned. Then, LEND(M ) is recur-sively called during HTN planning. However, according to our scenario, the attempt to make book b 2 accessible (after picking it up) will fail. At this point the GTP will backtrack all the way up to PICK(b 1 ) (third column) but not find a way to reposition the first book so as to make the second accessible. The system will then resort to HTN bactracking, which will choose the alternative method m 4 to give b 2 directly to the person. 3 According to our initial scenario, this will also fail even after the GTP backtracks to reposition b 1 (not shown in the figure). The HTN planner will then backtrack once again up the hierarchy and perhaps choose method m 4 to give b 1 directly to the person, after which it should be possible to make b 2 accessible and continue planning.

The last column of Figure 3 shows the mapping of the four "compound" GTP tasks in the third column into grasp and placement actions. A more interesting domain would be where these actions are encapsulated into one compound PICKMAKEACCESSIBLE(O, H) task (for object O and human H), instead of the two tasks PICK(O) and MAKEACC(O, H). This will allow the GTP to backtrack from PLACE(O) to GRASP(O), allowing failure to be detected early in HTN planning-when PICKMAKEACCESSIBLE(O, H) fails because a (future) GTP task/action (PLACE(O) in our example), due to be tried later by the HTN planner, is predicted by the GTP to be impossible. Such encapsulation can also minimise GTP backtracking by, from the outset, planning with respect to definite future GTP actions (e.g. planning the grasp with respect to the placement).

IV. IMPLEMENTATION

As mentioned in Section II, we have adapted an HTN planner and implemented a GTP. We have also sufficiently implemented the algorithms presented in this paper to gain some valuable insights. In our setup, the (real) PR2 is in a room with objects like tables, shelves, and chairs, and the same is modelled in 3D, onto which humans and objects (e.g. books) are dynamically projected whenever they are detected in the real room by respectively a Kinect (Microsoft) sensor, and PR2's stereo cameras coupled with a pattern-based marker detection module. For 3D visualization and planning we use the Move3D software [START_REF] Simeon | Move3d: a generic platform for path planning[END_REF].

Our current GTP implementation has some of the functionality depicted in Figure 3, including: (i) storing the sequence of GTP tasks pursued so far; (ii) basic backtracking to find an alternative solution for a chosen GTP task in the sequence; and (iii) computing predicates such as visible(O, A), reachable(O, A), on(O, O 2 ), inside(O, O 2 ) and coveredBy(O, O 2 ) for an agent A and objects O, O 2 , where the first two are computed based on the concept of mightability maps presented in [START_REF] Pandey | Mightability maps: A perceptual level decisional framework for co-operative and competitive human-robot interaction[END_REF]-which the authors showed to be computed and updated fast enough for online HRI-and the other facts using techniques from the geometric analysis of the 3D world model, and domain specific heuristics. 4We demonstrate our implementation in figures 4 and 5, where the second is essentially a screen dump of the visible(O, H) and reachable(O, H) shared literals computed. Figure 4 (a) is the initial state with two books on the table next to the PR2, and a small white platform in front of it to exchange objects. Planning starts with the PR2 picking (b) the grey book and making it accessible (c) to the human on the platform. The same is done for the white book in (d) and (e). The position of the white book, however, makes the grey one no longer visible to the human, which later makes it impossible to give the POS machine to him-in the current example this requires that all books be visible to him. Consequently, the GTP backtracks and finds a slightly different way to place the white book (f) so that both books are visible.

Figure 5 (a) shows that at the start, the grey book (Grey) and the white book (White) are not visible (Vis) nor reachable (Reach) to the human, as they both require an effort (E) of either 3 or 4, instead of 1. Figure 5 (d) shows how after backtracking and moving the white book, the grey one becomes visible once again. Note that something is deemed visible to a human based on a threshold on the percentage of pixels visible, using the approach presented in [START_REF] Marin-Urias | Towards shared attention through geometric reasoning for human robot interaction[END_REF]. Our threshold here is that at least 50% of an object should be visible to the human for the fact to hold.

V. EXPERIMENTAL RESULTS

To analyse the runtime performance of the combined HTN-GTP system we implemented and ran the domain depicted in Figure 2. Specifically, we implemented most HTN and GTP tasks in the domain except for NAVTO(Obj) (which requires further work), and we modified the HTN domain slightly by replacing PUTON(O 1 , O 2 ) with MAKEACC(O, H), and grouping PICK(O) together with the 4 other GTP tasks for reasons explained in Section III.

We ran the experiments on the PR2, which has two quadcore i7 Xeon processors (8 cores), 24 GB of memory, and a 500 GB hard drive. 5 We only analysed the performance of the HTN-GTP system with HTN backtracking alone-we did not exploit geometric backtracking; we intend to use these results as a baseline to compare against an extended HTN-GTP system being developed, which interleaves backtracking as shown in Figure 3. We ran the experiment 100 times, where each run started by calling the MANAGEORDER(M ) task in Figure 2. The initial state of the GTP was similar to that in Figure 4 except that there was also a POS machine. We kept the GTP initial state fixed: automatically generating initial states with different positions and orientations for books is left as future work. We do note, however, that manual adjustments to the GTP initial state did not seem to change the experimental results. The HTN initial state was such that the member had to always pay by credit card, which forced method m 7 to be selected-the one that relies on the GTP. 6The results are summarised in Table II. We note that HTN planning (alone) took negligible time. Observe that PUTAWAY(O, H) was the most "difficult" task to plan: the GTP could not find a solution 52% of the time, and it took 51 seconds on average, making it also the most computationally expensive task. On the contrary, the GTP always found a solution for GIVE(O, H), which was also the least computationally expensive task.

Although, intuitively, it should be possible to find solutions less often for GIVE(O, H) than for SHOW(O, H), this was not the case because GIVE(O, H) is followed by SHOW(O, H) in our HTN domain: hence if there is no solution for SHOW(O, H) then GIVE(O, H) will not be attempted, and if SHOW(O, H) does have a solution then it is quite likely that GIVE(O, H) will also have one, as they both rely on the ability to make an object visible. 7Interestingly, MAKEACC(O, H) and PUTAWAY(O, H) have similar results in their respective columns in the table, but the latter takes much longer to plan. This is due to different thresholds on visibility: for an object to be deemed accessible it is sufficient if (along with reachability requirements) at least 50% of the object's pixels are visible to the person, whereas for an object to be considered successfully put away, we have set that value to 0%. Since our GTP approach is constraint hierarchy based, the computation time is greatly affected by what stage in the planning process the planner fails. As pixel based visibility computation is relatively computationally expensive, it is left for the final stages of planning. It appears that with PUTAWAY(O, H), checking the feasibility of visibility constraints fails more times than with MAKEACC(O, H), as in most cases objects were not completely hidden-in fact, they were sufficiently visible.

The experiments revealed that our combined HTN-GTP domain was, in some sense, "complete"-the combination was almost always able to find HTN-GTP solutions for MANAGEORDER(M ), without frequent backtracking. There was only one HTN-GTP planning attempt that failed completely (with 8 backtracks), when the GTP could not put/hide away the POS machine-within the 60-second time limit we had set for GTP-despite all symbolic backtracking attempts. On average the symbolic planner backtracked about once (actually, 0.86 times) per run before finding a solution, with slightly under 10% of the total runs backtracking more than 3 times per run. This suggests that GTP backtracking should, perhaps, be done sparingly-rather than every time a GTP task being pursued has no solution-by relying more on HTN backtracking, albeit at the expense of completeness. Another tradeoff between completeness and efficiency is to significantly reduce the grasps and orientations tested by GTP tasks like MAKEACC(O, M ) to a few "good" ones that generally work well; the number of pixels tested when determining object visibility could also be reduced in a similar way. We believe that these improvements will make the combined system more practical for real-world applications.

VI. CONCLUSION

We have presented an approach to combining HTN and geometric task planning, which allows more sophisticated reasoning than possible with standard trajectory planning. The combination makes way for rich backtracking at multiple levels, and also interleaved backtracking. We showed how the two planners could be interfaced, and gave insights into a methodology for developing HTN-GTP domains. Our prototype implementation is able to do basic GTP backtracking, and to compute and share symbolic facts, which the HTN developer can use in preconditions. Finally, we presented experimental results that we intend to use as a benchmark to test future extensions, and for developing heuristics for the GTP.

Fig. 1 :

 1 Fig. 1: An overview of the geometric task planner (GTP).

  ) SAY(T ) MAKEBKACC(B, M ) ADD(B, M ) m4 AND DISPLAY(B, T, M ) m5 AND PICK(B) SHOW(B, M ) SAY(T ) GIVEBK(B, M ) WAITTAKE(B, M ) ADD(B, M ) TAKEPAYMENT(M ) OR m6 DEBITACC(M, N * cost) m7 AND PLACEPOSM(M ) OR m8 AND PICK(mac) SAY(swipe) PUTON(mac, stnd) m9 AND NAVTO(mac) PICK(mac) NAVTO(desk) SAY(swipe) PUTON(mac, stnd) PUTAWAYPOSM(M ) m10 AND SAY(thank) PICK(mac) PUTAWAY(mac, M ) EMAIL(M )

  M ) ∧ makeAcc(B, M ) ? {¬held(B, M ), lent(B, M )}, makeAcc(B, M ) - , makeAcc(B, M ) + WAITTAKE(B, M ) held(B, M ) ∧ gave(B, M ) {¬held(B, M ) ∧ ¬gave(B, M ) ∧ lent(B, M )} ADD(B, M ) lent(B, M ) ∧ numLent(M, N ) {¬numLent(M, N ), numLent(M, N + 1)} GIVEBK(B, M ) held(B, M ) ∧ give(B, M ) ? ∧ ¬hvy(B) {gave(B, M )}, give(B, M ) - , give(B, M ) + PICK(O) pick(O) ? pick(O) - , pick(O) + SHOW(O, M ) show(O, M ) ? show(O, M ) - , show(O, M ) + DEBITACC(M, Cost) cred(M, C) ∧ (C ≥ Cost) {¬cred(M, C), cred(M, C -Cost)} EMAIL(M ) lent(B, M ) {emailed(M )} PUTON(O1, O2) putOn(O1, O2) ? putOn(O1, O2) - , putOn(O1, O2) + PUTAWAY(O, M ) putAway(O, M ) ? putAway(O, M ) - , putAway(O, M ) + NAVTO(Obj)navT o(Obj) ? navT o(Obj) - , navTo(Obj) +

Fig. 3 :

 3 Fig. 3: Combined backtracking scenario for Figure 2.

Fig. 4 :

 4 Fig. 4: A Move3D scenario for the domain in Figure 2: making two books accessible by backtracking.

Fig. 5 :

 5 Fig. 5: Symbolic facts computed for Figure 4.

TABLE I :

 I The table for Figure2. The top half (above the thick line) are methods (M) and the bottom half are operators. For legibility, empty sets have been ommitted from the table.

TABLE II :

 II The table summarises, for each GTP task: the time taken

	to find a solution (time); what percentage of its planning attempts
	were successful (succ %); the total number of points tested in 3D
	space (pts); the total number of grasps tried (grasps); the total number
	of orientations tried (orts); and the total number of times the trajectory
	planner was called (calls).

We also use GTP as an abbreviation for geometric task planning.

We could also imagine more generic GIVEBK(B, M ) and MAKEBKACC(B, M ) actions that can handle any object type or give and make books accessible for reasons other than lending.

We assume that the book is light enough to be handed to the person.

Note that by deriving and using geometric states as shared literals we need to address the ramifications of geometric backtracking on already pursued symbolic actions. Due to space limits we leave our solution for another paper.

Running the HTN-GTP system on the PR2 allowed using real object and human locations for constructing the initial states for planning, and also directly executing plans found.

We invite the reader to view a video of a single run of the experiment at www.tinyurl.com/pr2-exp; it has been edited for easier viewing.

While GIVE(O, H) also needs O to be reachable to H in free space, in our scenario this is easy to achieve.

*This work was conducted within the EU SAPHARI project (www.saphari.eu) funded by the E.C. division FP7-IST under contract ICT-287513.


D D D Tran

V T Sironneau

J T Hodges

Raymond Armante

J Cuesta

H Tran
email: ha.tran@lmd.jussieu.fr

Prediction of high-order line-shape parameters for air-broadened O2 lines using requantized classical molecular dynamics simulations and comparison with measurements

published or not. The documents may come

Prediction of high-order line-shape parameters for air-broadened O2 lines using requantized classical molecular dynamics simulations and comparison with measurements

Introduction

It is now widely known that accurate and precise line-shape modeling is necessary to meet the requirements of laboratory measurements and a wide variety of applications (see [START_REF] Hartmann | Recent advances in collisional effects on spectra of molecular gases and their practical consequences[END_REF] and references therein, for instance). To this aim, it is recommended that the Hartmann-Tran (HT) [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF][START_REF] Ngo | Erratum to "An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF] profile be used for high-resolution spectroscopy [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC technical report)[END_REF] to replace the usual Voigt model. The HT profile accounts for various collisional effects affecting the measured line shape: the collision-induced line broadening and shifting and their speed dependences; the velocity changes due to collisions and the temporal correlation between changes in velocity and internal state. It was shown that this profile can model measured transitions of various molecular systems to within a few 0.1 % (e.g. [START_REF] Bui | Observations of Dicke narrowing and speed dependence in air-broadened CO2 lineshapes near 2.06 μm[END_REF][START_REF] Long | Frequency-agile, rapid scanning cavity ringdown spectroscopy (FARS-CRDS) measurements of the (30012)←(00001) near-infrared carbon dioxide band[END_REF][START_REF] Lin | Cavity ring-down spectrometer for high-fidelity molecular absorption measurements[END_REF][START_REF] Sironneau | Line shapes, positions and intensities of water transitions near 1.28 μm[END_REF][START_REF] Fasci | Dual-laser absorption spectroscopy of C2H2 at 1.4 μm[END_REF][START_REF] Kowzan | Line positions, pressure broadening and shift coefficients for the second overtone transitions of carbon monoxide in argon[END_REF][START_REF] Ngo | Spectral shapes of rovibrational lines of CO broadened by He, Ar, Kr and SF6: A test case of the Hartmann-Tran profile[END_REF][START_REF] Odintsova | Highly accurate intensity factors of pure CO2 lines near 2 μm[END_REF][START_REF] Lisak | Application of the Hartmann-Tran profile to analysis of H2O spectra[END_REF]). The international spectroscopic database HITRAN [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] now provides parameters of this profile when available. These lineshape parameters are usually obtained from fits of laboratory measured spectra. However, correct use of the HT profile for spectra analysis requires two key conditions. First, because of the large number of line-shape parameters involved, a multi-spectrum fitting technique applied to spectra measured over a large pressure range is recommended in order to avoid numerical correlation between various parameters. Second, high signal-to-noise ratio spectra are needed to accurately retrieve all the line-shape parameters. Both conditions are not easily met for many molecular systems, over wide spectral ranges and for various pressure and temperature conditions. Therefore, addressing the precision and accuracy requirements of wide-ranging applications as well as populating spectroscopic databases with HT parameters constitutes a huge amount of experimental and data analysis effort.

In parallel with precise and accurate laboratory measurements, theoretical calculations can be used to predict high-order line-shape parameters (i.e. parameter characterizing refined effects such as the speed dependence of the collisional width, the collision-induced velocity changes). In [START_REF] Ngo | A strategy to complete databases with parameters of refined line shapes and its test for CO in He, Ar and Kr[END_REF][START_REF] Ngo | Precise predictions of H2O line shapes over a wide pressure range using simulations corrected by a single measurement[END_REF], it was shown that first-principles calculations based on molecular configurations and intermolecular potentials, combined with a limited amount of information obtained from measurements successfully predicts the shapes of CO and H2O ro-vibrational lines. Indeed, these theoretical calculations are based either on classical molecular dynamics simulations (CMDS) [START_REF] Ngo | A strategy to complete databases with parameters of refined line shapes and its test for CO in He, Ar and Kr[END_REF] or a combination of CMDS and semi-classical methods (see [START_REF] Ngo | Precise predictions of H2O line shapes over a wide pressure range using simulations corrected by a single measurement[END_REF] and references therein). It was shown that the non-Voigt effects observed in the measured spectra are well predicted by these first-principles calculations, for various molecular systems (e.g. [START_REF] Hartmann | Abinitio calculations of the spectral shapes of CO2 isolated lines including non-Voigt effects and comparisons with experiments[END_REF][START_REF] Lamouroux | Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements[END_REF][START_REF] Le | Molecular dynamic simulations of N2-broadened methane line shapes and comparison with experiments[END_REF][START_REF] Larcher | CO2 isolated line shapes by classical molecular dynamics simulations: Influence of the intermolecular potential and comparison with new measurements[END_REF][START_REF] Tran | An isolated line-shape model based on the Keilson-Storer function for velocity changes. II. Molecular dynamics simulations and the Q(1) lines for pure H2[END_REF][START_REF] Tran | Velocity effects on the shape of pure H2O isolated lines: Complementary tests of the partially correlated speeddependent Keilson-Storer model[END_REF]) although the difference between the computed and measured line widths could be several percent. In [START_REF] Ngo | A strategy to complete databases with parameters of refined line shapes and its test for CO in He, Ar and Kr[END_REF][START_REF] Ngo | Precise predictions of H2O line shapes over a wide pressure range using simulations corrected by a single measurement[END_REF], the calculations were thus empirically improved by introducing a measured value of the line width into the computed auto-correlation function of the transition dipole moment, where the line-shape equals the Fourier-Laplace transform of the latter quantity. With this correction procedure, it was shown that the calculations can predict measured spectra of several lines of CO [START_REF] Ngo | A strategy to complete databases with parameters of refined line shapes and its test for CO in He, Ar and Kr[END_REF] and H2O [START_REF] Ngo | Precise predictions of H2O line shapes over a wide pressure range using simulations corrected by a single measurement[END_REF] over a large pressure range to within 1 %, significantly better than the best fits of the measurements with the usual Voigt profile. In this work, first-principles CMDS calculations of line-shapes were used to provide theoretical spectra from which high-order line-shape parameters could be retrieved. Specifically, we determined the (quadratic) speed dependence of the line broadening and the Dicke narrowing parameter by global multi-spectrum fitting of HT profiles to CMDScalculated spectra. This procedure is applied and validated, in this work, for air-broadened absorption spectra of O2. Absorption by O2 is very important in atmospheric applications because the molar fraction of O2 in dry air is nearly constant and well known. The optical interrogation of O2 absorption lines therefore allows accurate determination of the atmospheric airmass (pathlength) traversed by the measured photons. This measurement can reduce errors caused by uncertainties in airmass associated with simultaneous measurements of other gases of scientific interest (e.g. CO2, CH4), for instance. Therefore, precise spectroscopic parameters of O2 are required in order to retrieve reliable results from atmospheric observations. The remainder of this paper is divided into three sections. The theoretical simulations and measurements are briefly described in Sec. 2. Multi-spectrum fits of the HT profile to theoretical and experimental spectra as well as theoretical predictions of the temperature dependence of certain line parameters are discussed in Sec. 3. Finally, we give concluding remarks in Sec. 4.

Data used and analysis procedure

Requantized classical molecular dynamics simulations (rCMDS)

Classical molecular dynamics simulations (CMDS) [START_REF] Allen | Computer simulations of liquids[END_REF] were carried out for the O2 (20 %) and N2 (80 %) mixture at 203 kPa and three temperatures: 200 K, 250 K and 296 K using the same calculations as those of [START_REF] Lamouroux | Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements[END_REF][START_REF] Hartmann | Collisional broadening and spectral shapes of absorption lines of free and nanopore-confined O2 gas[END_REF] where details on the calculations procedure can be found. The intermolecular potentials used were described by pairwise 6-12 Lennard-Jones atom-atom contributions, complemented by Coulombic forces between fictitious charges that were introduced to reproduce the electric quadrupoles of the molecules. The atom-atom data for O2-O2 and N2-N2 were taken from Refs. [START_REF] Hartmann | Collisional broadening and spectral shapes of absorption lines of free and nanopore-confined O2 gas[END_REF] and [START_REF] Bouanich | Site-site Lennard-Jones potential parameters for N2, O2, H2, CO and CO2[END_REF], respectively, and the corresponding parameters for O2-N2 were deduced from the standard combination rules [START_REF] Hirschfelder | Molecular Theory of Gases and Liquids[END_REF]. During the CMDS, the force and torques applied to each molecule by its surrounding neighbors are computed classically. This provides the center-of-mass position and velocity, the molecular axis and the rotational momentum for each molecule at each time. The autocorrelation function of the dipole moment (along the molecular axis) can thus be computed, its Fourier-Laplace transform directly yields the corresponding normalized absorption band spectrum. The requantization procedure of Ref. [START_REF] Hartmann | Abinitio calculations of the spectral shapes of CO2 isolated lines including non-Voigt effects and comparisons with experiments[END_REF] was applied here by matching the classical rotation frequency of the molecules to the quantum position of P branch lines. The electronic spin of O2 was neglected, as done in Refs. [START_REF] Hartmann | Abinitio calculations of the spectral shapes of CO2 isolated lines including non-Voigt effects and comparisons with experiments[END_REF][START_REF] Lamouroux | Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements[END_REF]. The rotational quantum number is thus equal to the total rotational quantum number and PP and PQ transitions are identical (as for RR and RQ lines). Note that our rCMDS do not take into account the dephasing of the dipole, which is associated with the fact that the effects of intermolecular interactions for molecules in the upper and lower states of the optical transitions are different. Consequently, the calculated spectra do not show any pressure shift.

The calculations were performed with the IBM Blue Gene/P computer † of the Institut du Dévéloppement et des Ressources en Informatique Scientifique. For each temperature condition, calculations were made for 122.88×10 6 molecules. The molecules were initially randomly distributed in 4096 cubic volumes with periodic conditions, with each volume containing 30,000 molecules. For each temperature condition, twelve values of the Doppler width, ranging from 0.012 cm -1 to 0.53 cm -1 , were used in the calculations. This set of parameters provided a large range for the ratio (i.e. from about 0.075 to 4.606) covering the near-Doppler broadened to collisional-broadened regimes.

Experimental data

The measured spectra of Ref. [START_REF] Lamouroux | Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements[END_REF] of air-broadened 16 O2 lines in the singlet  band [ ] were retained here for validation of the procedure that we have proposed. Measurements were made at room temperature and for various pressures ranging from 6.7 kPa to 100 kPa (Table 1). These experiments were done at the National Institute of Standards and Technology (NIST) and were based on the frequency-stabilized cavity ringdown spectroscopy (FS-CRDS) technique described in [START_REF] Hodges | Frequency-stabilized single-mode cavity ringdown apparatus for high-resolution absorption spectroscopy[END_REF][START_REF] Long | Frequency-stabilized cavity ring-down spectroscopy[END_REF]. The ring-down cavity was actively length-stabilized and had a mirror-to-mirror distance of 74 cm, with an effective mirror intensity reflectivity equal to 0.99995 and a minimum detectable absorption coefficient † Manufacturers and commercial product names are given solely for completeness. These citations do not imply recommendation or endorsement by NIST based on a 1 s averaging time of 2×10 -10 cm -1 . The same mixture of synthetic dry air (79.28 % N2, 20.72 % O2 by volume) was used for all measured spectra. The maximum single-pass absorbance levels were all less than 10 -4 cm -1 . The relative combined standard uncertainties in O2 molar fraction, absolute temperature and sample pressure were less than 0.01 %, 0.02 % and 0.05 %, respectively. We measured seven lines for which the temperature of the measurement was almost constant (i.e. variation within 0.5 K) for all considered pressures. The value of the rotational quantum number of these absorption lines spanned from 1 to 13 (Table 1), thus providing a meaningful test of the calculations. More details of the particular FS-CRDS setup and the measurement procedure can be found in [START_REF] Lamouroux | Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements[END_REF] and [START_REF] Sironneau | Line shapes, positions and intensities of water transitions near 1.28 μm[END_REF].

Analysis procedure

We first fit the HT profile to the rCMDS-calculated (or measured) spectra. Because of the large number of involved parameters, a constrained global fitting procedure was used. For each line, the line broadening coefficient , the speed dependent component , and the Dicke narrowing parameter , were constrained to be the same for all considered Doppler widths (or pressure conditions), where all three parameters have dimensions of wave number per unit pressure. For each spectrum, the line position and line intensity were fitted individually, together with a linear base line. For the measured spectra, the speed dependent component of the pressure shift was also fitted while this quantity was fixed to zero for those spectra calculated by CMDS, because the pressure shift was totally neglected in the theoretical calculations. The Doppler widths were fixed to values computed at the temperature of the rCMDS or to those of the measurements. For the latter, the measured temperatures at each pressure condition were used for the determination of the Doppler widths and not the average temperature over all pressures. Both the calculated and measured spectra were normalized by their peak absorption in the fitting procedure. Because of the limited signal-tonoise ratio of both the calculated and measured (i.e. about 500 and 2000, respectively) spectra, it was impossible to retrieve all the parameters of the HT profile. Therefore, we chose to fix the correlation parameter to zero, with the resulting reduced form of the HT profile being equivalent to the quadratic speed dependent hard-collision profile. Note that the assumption of no correlation between velocity-and internal-state-changing collisions, is justified for systems for which the kinetic collision frequency, deduced from the mass diffusion coefficient is much smaller than the broadening frequency (i.e. broadening coefficient), as the case here for the O2 lines considered here [i.e. 6 kHz Pa -1 (0.02 cm -1 /atm) [START_REF] Long | O2 A-band line parameters to support atmospheric remote sensing[END_REF] compared to 15 kHz Pa -1 (0.05 cm -1 /atm) (see Table 2)].

As demonstrated previously for O2 [START_REF] Lamouroux | Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements[END_REF][START_REF] Hartmann | Collisional broadening and spectral shapes of absorption lines of free and nanopore-confined O2 gas[END_REF] and for other molecular systems [START_REF] Ngo | A strategy to complete databases with parameters of refined line shapes and its test for CO in He, Ar and Kr[END_REF][START_REF] Hartmann | Abinitio calculations of the spectral shapes of CO2 isolated lines including non-Voigt effects and comparisons with experiments[END_REF][START_REF] Le | Molecular dynamic simulations of N2-broadened methane line shapes and comparison with experiments[END_REF][START_REF] Larcher | CO2 isolated line shapes by classical molecular dynamics simulations: Influence of the intermolecular potential and comparison with new measurements[END_REF][START_REF] Tran | Spectral shapes of Ar-broadened HCl lines in the fundamental band by classical molecular dynamics simulations and comparison with experiments[END_REF], the non-Voigt effects observed on the rCMDS-calculated spectra are in very good agreement with those of measured spectra (through comparison of their Voigt fits residuals and parameters). However, line broadening coefficients predicted by rCMDS can be significantly different from measured values. For O2, it was shown that [START_REF] Hartmann | Collisional broadening and spectral shapes of absorption lines of free and nanopore-confined O2 gas[END_REF] broadening coefficients obtained from fits of rCMDS spectra with Voigt profiles are about 8 % lower than those obtained from measurements using this same profile. In this work, we observed that by using the HT profile the values of obtained from rCMDS are on average 2 % smaller than the measured values. Hence, we use rCMDS here to predict only the high-order line-shape parameters and not the line broadening coefficient. In the second step, we therefore refit the measured spectra while constraining the speed dependence of the line width,  and the Dicke narrowing parameter, , to those obtained from fits of the rCMDS spectra. We then compared the quality of the fits as well as the obtained parameters to the previous case when we fit all the parameters. Finally, note that we also used a Voigt profile to fit the measured spectra for comparison.

Results and discussion

In the following, we denote by VP all results obtained from fits of the measurements with the Voigt profile, by HT those obtained from fits of measurements with the HT profile when all line parameters were adjusted, and by HT_fix all results obtained from fit of measurements with the HT profile but with 2 and vc fixed to those obtained from rCMDS.

Fit residuals and retrieved line-shape parameters

Fig. 1 shows the measured absorption spectra of the R1Q2 and P5P5 transitions (first row) at various values of the total pressure and the fit residuals obtained with VP, HT and HT_fix cases, respectively. As can be observed on this figure, the VP leads to relatively large residuals with magnitudes reaching as much as 3 % of the peak absorption. As expected, the residuals obtained with the HT profile are relatively small, almost within the experimental noise, regardless of the considered pressure. When fixing the values of 2 and VC to those obtained from rCMDS (i.e. the HT_fix fitting procedure), the corresponding fit residuals are close to the previous case in which all parameters are adjusted. As an example, the standard deviations of the fits obtained for the R1Q2 (left side of Fig. 1) using VP, HT and HT_fix are 3.816 10 -6 , 0.451 10 -6 and 0.473 10 -6 , respectively. These results show that one can determine the high-order HTP parameters by fitting the HTP to the rCMDS-calculated line-shape.

The maximum-to-minimum amplitudes of residuals (relative to the peak absorption of unity) obtained from fits of the seven measured lines with VP, HT and HT_fix as a function of pressure are plotted in Fig. 2. As shown, employing a Voigt profile leads to residuals significantly higher than the other two cases. Moreover, the use of parameters obtained from rCMDS provides a precise description of the measured spectra for all considered lines and pressure conditions. Indeed, results obtained with HT_fix are almost as good as those obtained when all parameters of the HT profile are fitted, with maximum relative fit residuals well below 1%.

Table 2 lists the line-shape parameters obtained from fits of the measurements using the HT and HT_fix models. First, comparisons between the values of and obtained from measured spectra and those deduced from rCMDS show that they are rather close. For most of the considered lines, values of obtained from rCMDS are slightly larger than those of the measurements while the opposite trend is observed for . This result indicates that there are some correlations between these two parameters, and their values do not totally reflect the corresponding physical phenomenon. Note also that larger differences are observed for for weak lines (i.e. R1Q2, P11P11 and P13P13 lines, see Table 2). This is probably due to the smaller signal-to-noise ratio of the corresponding spectra and the weak influence of on the line shape. Nevertheless, as can be observed in Fig. 2, the two sets of line-shape parameters lead to very good agreements with measured spectra for a wide pressure range. Concerning the line broadening coefficient, 0, the values obtained with the HT and HT_fix fitting procedures are very close to each other. Similarly, the obtained (small) values of the speed dependence component of the line shift are quite independent of the fitting procedure used. 2. Line-shape parameters for the seven considered transitions obtained from multi-spectrum fitting the HT (non-italicized) and the HT_fix (italicized) models to the measured spectra, respectively. All parameters have units of kHz Pa -1 , which can be converted to commonly used cm -1 atm -1 units using the conversion factor: 0.003379838 (cm -1 atm -1 )/(kHz Pa -1 ). The parenthetical values are multiples of the last significant digit and correspond to three times the standard deviation obtained from the fits. "*" indicates that the parameter was obtained from fits of the rCMDS-calculated spectra and subsequently fixed in the fit to the measurements.

Figure 3 shows the ratio of the line intensities obtained with the HT_fix and VP to those deduced from the HT. As widely known, the line intensity retrieved with the Voigt profile strongly depends on the considered pressure. Here the difference between the fitted VP and that determined by using the HT profile can reach 1.5 % relative to the peak absorption.

Using the HT_fix fitting procedure leads to very similar results as for HT with a maximum relative difference of about 0.3 %. These results show that the HT_fix satisfactorily models the measured spectra of all air-broadened O2 lines considered here for atmospheric pressure conditions. Therefore, rCMDS can be used to predict high-order line-shape parameters.

We also analyzed measured spectra where we constrained the values of and to those predicted by rCMDS and where we fit the individual spectra corresponding to a single pressure. Our analysis shows that the retrieved value of for each pressure condition is very close (within 0.5%) to that obtained previously by global fits to all the measured spectra. These differences in the value of lead to a derivation on the calculated line shapes of typically a few 0.1 %. The best overall agreement is obtained when is deduced from spectra measured in the near collision regime (i.e.

). For comparison, the pressure dependence of the O2 broadening coefficient obtained from a simple-fitting procedure using the Voigt profile can differ from that obtained using the HTP by as much as 10 % [START_REF] Lamouroux | Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements[END_REF]! These results demonstrate that with the rCMDS-predicted and parameters, a single spectrum, measured in the collision regime, can be sufficient to determine the line-broadening coefficient with a relative precision much better than 1 %.

Temperature dependences of line-shape parameters

From the results obtained previously at room temperature, we extended our rCMDS to various temperatures (see Sec. 2.1) to predict variation of the line-shape parameters with temperature, which are crucial for atmospheric applications. Firstly, the room temperature line-shape parameters were constrained to those obtained previously from fits of the HT profile to room-temperature rCMDS spectra. Only their relative temperature dependences were adjusted in the fit of rCMDS spectra at 200 and 250 K. The usual power law for the temperature dependence of the line broadening was adopted here for , and . Starting from T0 = 296K, we can thus compute values at a temperature T as: , in which is either , or and n the temperature dependence. Note that again we used a global multi-spectrum fitting procedure in which the temperature dependences of , and were constrained to be the same for each corresponding value of the Doppler width (see Sec. 2.1). Based on several analyses, we found that we cannot simultaneously fit the temperature dependences of VC and of . This problem may be caused by the limited signalto-noise ratio of our calculated spectra and by numerical correlation between these parameters. Therefore, as explained in Ref. [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF], we assumed here that is proportional to , thereby constraining the temperature exponent of to be unity. The obtained results for the temperature dependences of and as well as the values of the latter at room temperature are reported in Table 3. Although we do not have any non-room-temperature spectra to directly compare with the predicted results, the latter can be compared to literature data. The predicted temperature exponent parameter for the line broadening was compared with experimental results of [31] in which the temperature exponents of self-and N2broadening coefficients for the O2 A band lines were reported to be about 0.8. Our calculated values are in good agreement with these measurements. For the temperature dependence of , no comparison can be made because, to the best of our knowledge, no measured data are available. Large line-to-line variation of is observed for P1 and for high J lines (Table 3). This variation cannot be physically meaningful and probably due to the small signal-tonoise ratio of the calculated spectra for these lines. Higher signal-to-noise ratio spectra, computed using much larger number of molecules in rCMDS, are thus needed to better predict this parameter. and the temperature dependences of and retrieved from rCMDS-calculated spectra. The parenthetical values are multiples of the last significant digit and correspond to three times the standard deviation obtained from the fits. The parameters , and have units of kHz Pa -1 , which can be converted to commonly used cm -1 atm -1 units using the conversion factor: 0.003379838 (cm -1 atm -1 )/(kHz Pa -1 ).

Conclusion

High-order line-shape parameters are required when using refined line-shape models such as the recently recommended Hartmann-Tran profile. However, a huge amount of experimental and analytical effort is required to determine these parameters from rovibrational and rovibronic molecular spectra of relevant species. In this work, we have shown that these line-shape parameters can be accurately predicted by using requantized classical molecular dynamics simulations. Specifically, these rCMDS were used to compute normalized absorption spectra of several air-broadened O2 lines, and the simulated spectra were subsequently fit using the Hartmann-Tran profile, with the high-order line-shape terms treated as adjustable parameters. Using a FS-CRDS apparatus over a large pressure range, the resulting line-shape parameters were then used to constrain the HT profile analysis of measured spectra. We found this approach to be significantly better than fitting the Voigt profile to the measured spectra and almost as good as when all the parameters of the HT profile were fitted to the measured spectra. We also show that, providing that the high-order line-shape parameters are correctly predicted, only one spectrum, measured in the collision regime is needed to deduce the entire set of line-shape parameters. This opens the route for the prediction of high-order line-shape parameters for various molecular systems and their inclusion in spectroscopic databases using rCMDS, provided that reliable potentials are available. Finally, rCMDS calculations were also used to deduce the temperature dependences of the line broadening coefficients and the associated speed dependent components. The quality of the prediction could be probably improved by improving the signal-to-noise ratio of the calculated spectra through using larger number of molecules in the rCMDS. These results motivate new measurements for various temperature conditions required to validate these predictions.

Figure captions

Fig. 1 :

 1 Fig.1: Measured absorption spectra of two air-broadened O2 lines in the band measured by FS-CRDS at three total pressures (first row) and the corresponding residuals obtained from fitting the VP (second row), the HT and HT_fix (third and fourth rows), respectively.

Fig. 2 :

 2 Fig.2: Maximum-to-minimum amplitudes of residuals obtained from fits of all the seven considered lines with the VP, HT and HT_fix vs total pressure.

Fig. 3 :

 3 Fig. 3: Ratio of the line intensities obtained with the VP (left) and the HT_fix fitting procedure (right) to those deduced from the use of the HT model, versus pressure.

Table 1 :

 1

	Line	Line center (cm -1 )	Temperature ( o C)	Pressure (kPa)	Maximum absorbance (10 -5 /cm)
	R1Q2	7889.933104	24.8	46.7; 60.0; 73.2; 86.6; 99.9 6.68; 13.4; 20.0; 26.7; 33.3;	3.6
	R3Q4	7895.477670	25.3	6.70; 13.4; 20.0; 26.7; 33.4	8.1
	R5Q6	7900.826802	25.3	6.70; 10.0; 13.4; 16.7	9.3
	P5P5	7867.653563	25.6	6.70; 13.4; 20.1; 26.7	4.2
	P9P9	7855.130970	25.0	73.2; 86.7; 99.8 6.71; 10.0; 13.3; 20.0; 60.0;	8.8
	P11P11	7848.636972	22.3	40.3 6.67; 10.0; 13.3; 26.6; 33.3;	8.3
	P13P13	7841.986547	24.9	60.0; 73.2; 86.6; 99.9 6.65; 13.3; 20.0; 33.3; 46.7;	8.1

Experimental conditions for the measured [ ]

16

O2 transitions considered in this work.

Table 3 :

 3 Room temperature values of , and

Acknowledgments: We thank J.-M. Hartmann for providing the original computational code of CMDS for oxygen and the Institut du Développement et des Ressources en Informatique Scientifique (IDRIS) for giving access to the IBM Blue Gene/Q parallel computer. Authors from LMD were supported by the French Space Agency, Centre National d'Etudes Spatiales. J.T. Hodges and V.T. Sironneau acknowledge support from the NIST Greenhouse Gas and Climate Science Program.