Phu Dao-Le Flécher

Nirjhar Nigam
email: nirjhar.nigam@icn-artem.com

Sondes Mbarek
email: sondes.mbarek@imt-bs.eu

Accounting for crypto-assets: A comparative analysis and overview of accounting rules and practices

Keywords: Crypto-assets, digital assets, cryptocurrency, blockchain, accounting recognition, disclosures, risks, IFRS, GAAP

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INTRODUCTION

Cryptocurrency 1 is gaining traction in the global markets and reaching at $876 billion as of December, 20222 . The year 2021/2022 also witnessed the rise of NFTs (Non-Fungible Tokens) and DeFi (Decentralized Finance) projects. Crypto investments of MicroStrategy and Tesla continued to draw the attention of investors and media. Musk's investment of $1.5 billion in the cryptocurrency brings Bitcoin into the mainstream and reveals the digital currency hole in the U.S. accounting rulebook.

The crypto investments matter to analysts, readers of company's financial statements, as well as to stakeholders including National Standard Setters (NSS), regulators, policymakers and academics. Tesla explained the accounting treatment in its 2021 annual filing, and warned investors that impairments to the value of its Bitcoin could hit its earnings. Take the case of software company MicroStrategy, which claims to be the world's largest publicly traded holder of bitcoins, holding some 125,000 of them. At current market rates, that is worth around $5 billion. In its fourth-quarter result of the 2021 period, it reported a bitcoin write-down of $146.6 million. Adjustments to their values are made only for price declines and no interim upward adjustments to reflect value gains are allowed until the assets are sold.

In Europe, the EFRAG research feedback indicated that large, listed companies have limited exposure to crypto-assets holdings (EFRAG Discussion Paper -July 2020). Furthermore, the International Accounting Standards Board (IASB) highlighted in its staff paper issued in November 2019 that only a small number of large IFRS reporting companies have reported crypto-assets and holdings of those assets among IFRS companies are insignificant (IFRS Foundation, IASB Staff Paper -November 2019). Nevertheless, crypto ecosystem and transactions are rapidly evolving, and we can reasonably expect that more companies will deal with various types of crypto-assets in the future.

Given the ongoing evolution, growth potential and diversity of crypto-assets as so as their unique and risky nature, there are intensive debates on the accounting treatment by holders and issuers of crypto-assets at the international level. And as the technology continues to evolve, it 1 Common terms used when discussing crypto-assets include cryptocurrency, coin, token, stablecoin, digital asset, and NFTs. As the accounting literature often calls digital assets as crypto-assets recognised in the financial statements, ''cryptocurrencies'', ''digital assets'' and ''crypto-assets'' are used interchangeably in this paper.

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is still not clear how to apply accounting requirements to transactions related to cryptocurrencies and digital tokens [START_REF] Fernandes | Defining issues: Blockchain and digital currencies challenge traditional accounting and reporting models[END_REF].

The first issue is the definition and the classification of digital assets that are important for their legal taxation and accounting treatments [START_REF] Strader | Digital Product Management, Technology and Practice: Interdisciplinary Perspectives, Published in the United States of America by Business Science Reference[END_REF]. Are cryptocurrencies defined as assets in accounting? What type of assets are they? Assets are clearly defined by accounting standards as resources owned or controlled by an entity due to past transactions or events, and are expected to generate economic benefits for the entity. But according to [START_REF] Kang | Research on Accounting and Application of University Digital Assets[END_REF], digital assets are by no means equivalent to intangible assets, because digital assets are not directly invested in production activities and cannot bring direct inflows of economic benefits. Unlike most commonly known intangible assets (e.g. software, intellectual property, brands), they have some cash-like properties; some are traded in active markets and they can have trading or investment asset attributes (EFRAG Discussion Paper -July 2020). In this sense, cryptocurrencies should be classified in short-term assets and placed close to cash and cash equivalents in the balance sheet (Luo and Yu 2022).

A second issue associated with the accounting for digital assets is measurement and valuation.

If digital products are capitalized, their initial value and subsequent valuation basis should be determined. Given the risky nature of cryptocurrencies, the use of subsequent valuation models at cost or at fair value can have significant impacts on companies' key financial ratios. Where digital products are capitalized, depending on the categorization of digital products as an inventory or a long-lived intangible asset, amortization and depreciation issues arise. For the amortization of digital products, the useful life of the digital products should be determined.

Another important issue is the classification of cash flows generated by crypto transactions.

Finally, disclosures of crypto-assets and associated risks should be addressed.

At the regulatory level, legislation relating to crypto-assets varies from one country to another.

In a recent study, the Cambridge Center for Alternative Finance (Cambridge CAF 2019) reviews various regulations relating to crypto-assets in 108 jurisdictions. The analysis of regulatory requirements shows that there is heterogeneity, but also a lack of clarity on the regulatory framework applicable to crypto-assets in different countries. The publication issued by the International Monetary Fund (IMF) in January 2020 highlights that although 64% of regulators have identified a gap in the regulation of crypto-assets, only 30% have closed this gap.

Taking into account the issues raised above, the objectives of this research are to carry out an exploratory study of regulatory frameworks applicable to crypto-assets in different countries (EU, UK, US and Asia). Given the potential growth and the diversity of crypto-assets as so as their unique and risky nature, many actors advocate for a consistent regulation of legal, financial, accounting and taxation aspects to oversee transactions related to crypto-assets. In the first step of the research, we carry out a comparative study on existing rules of accounting for crypto-assets that are put in place in different countries (EU, UK, US and Asia). Consistent accounting regulation is necessary in order to reflect the economic substance of each transaction and to anticipate future developments in this area. In the second step, we carry out an exploratory study of current accounting practices on a sample of companies who hold and issue crypto-assets in the EU, UK, US and Asia for the most recent reporting periods (2021 and 2022). A such study is required to shed light on the impact of ongoing and future evolutions of blockchain technology applications on the accounting for digital assets.

Our objective is to identify the best practices that exist and to come up with a list of recommendations that can be useful to policy makers, accounting standard setters and other market participants. To the best of our knowledge, this research will be the first cross-country comparative study expanding to US, UK, EU and Asian countries.

The rest of the paper is organised as follows.

Research methodology

The purpose of this study is to draw up an overview of current accounting practices relating to crypto-assets. Our research is deliberately exploratory [START_REF] Cornelius | Entrepreneurship studies: the dynamic research front of a developing social science[END_REF][START_REF] Busenitz | Entrepreneurship research in emergence: past trends and future directions[END_REF][START_REF] Aldrich | Blinded by the cities? Has there been progress in entrepreneurship research[END_REF] given the nascent nature of the topic. Exploratory data methodology involves the process of analysing data to identify patterns, trends, and relationships in the data without any preconceived notions or hypotheses and is considered appropriate for evolving topic. It is an iterative process that involves visualizing the data, summarizing it, and using descriptive statistics to identify features of the data that may be of interest. By exploring the data in a systematic and unbiased way, we can uncover hidden insights that can inform subsequent analyses and improve our understanding of the underlying data. Therefore, exploratory data methodology is a critical first step in our empirical analysis as it helps to answer our research questions and generate meaningful interpretations.

To achieve this goal, we will study how crypto-assets are classified, measured, recognized and disclosed in Europe, US, Asia and Australia.

In the first step, we make a literature review of current regulatory frameworks of blockchain technology applications as well as of existing accounting rules and practices. In order to explore the regulatory frameworks across countries where crypto-assets are largely prevalent, we use information from cryptocurrency platforms and on internet sources to find the top public companies for crypto trading, investment, mining, staking and other related crypto business models. In the second step, we extract the information related to these companies in order to build up our data collection model. Then we collect the annual financial reports of these companies for the 2021 and 2022 periods from their website or where they make annual filing (for example for US companies from https://www.sec.gov/edgar/ database).

Most of the data related to accounting and disclosures of crypto-assets comes from relevant sections such as balance sheets, profit and loss statements, cash flow statements, notes to the financial statements, notes related to accounting policies and management discussion and analysis section. The data is then extracted from these sections and structured into a database for further analysis. To ensure the accuracy and timeliness of the data collected, we verified the data amongst ourselves and adopted systematic approach to data extraction, quality assurance, and validation. Overall, this methodology for collecting information from annual reports is critical for the understanding of how cryptocurrency is measured, recognized and disclosed in respective countries as per their respective business model. The empirical observation of current accounting practices used by companies in different regions and under different GAAP can help regulators, standard setters, investors and other stakeholders make informed decisions about the measurement, recognition and disclosure of crypto-assets.

Overview of cryptocurrency ecosystem

Cryptocurrency as an application of blockchain technology

The global market for cryptocurrency stands at $876 billion as of December, 2022 2 . Bitcoin and Ethereum continue to dominate the trading volume: Bitcoin at 36.9% and Ethereum at 16.9%.

According to the statistics provided by CoinGecko, there are nearly 13,081 cryptocurrencies3 .

Each of these cryptocurrencies has its own features and characteristics that constantly evolve, which makes understanding and accounting for them particularly challenging. Bitcoin is the first cryptocurrency that was developed in 2009 and that was coined (Albrecht et al. 2019). The term 'cryptocurrency' is used because all transactions and issuance of new units will use the cryptography system that is developed using the blockchain technology.

A blockchain is a decentralized, digital ledger that records transactions across a network of computers (Corbet et al. 2019;Abramova & Bohme, 2016). It is used to store and record data in a way that is secure, transparent and tamper-proof. A blockchain is made up of a series of blocks, each of which contains a number of transactions [START_REF] Trivedi | Systematic Literature Review on Application of Blockchain Technology in E-Finance and Financial Services[END_REF]). These blocks are linked together in a chronological chain, that is called blockchain.

One of the key features of a blockchain is that it is decentralized, which means that it is not controlled by any single entity. Instead, it is maintained by a network of computers that work together to validate and record transactions. This decentralization makes it difficult for any single person or group to alter or corrupt the data stored on the blockchain [START_REF] Trivedi | Systematic Literature Review on Application of Blockchain Technology in E-Finance and Financial Services[END_REF].

Another key feature of blockchain technology is its transparency. Transactions on a blockchain are recorded and visible to anyone on the network, making it a highly transparent and accountable system. These features have accelerated the growth of blockchain market in current years (Iansiti and Lakhani, 2017;Yli-Huumo et al., 2016;Bohme et al., 2015). This market is expected to grow even further by 2025 to a business amounting 39 billion dollars (Statista, 2020).

Blockchains can be used for a wide range of applications, including digital currency, supply chain management, voting systems, and identity verification (Novo, 2018;Reyna et al., 2018;Jaoude & Saade, 2019). The most well-known blockchain is the one underlying the Bitcoin cryptocurrency, but there are also other blockchain networks such as Ethereum, Ripple, Litecoin, and many others. Also, Blockchain is the cryptocurrency's backbone technology, which may be thought of as an append-only register where transactions are recorded (Zhong et al. 2019;[START_REF] Trivedi | Systematic Literature Review on Application of Blockchain Technology in E-Finance and Financial Services[END_REF]. Blockchains are used as registers of transactions in cryptocurrency systems like Bitcoin and Ethereum, where the blockchain keeps track of current status and previous transactions (Janssen et al., 2020). The intended function of the Bitcoin was to be a universal medium of payment that replaces the currency of a certain country (DeVries 2016).

Cryptocurrency is also known as virtual currency or digital currency (Adam 2017).

While most of the cryptocurrencies are largely based on the bitcoin principles, they still have distinct features, functions and utility (Albrecht et al. 2019). Some cryptocurrency can be used as means of payment to facilitate transactions (like bitcoin, litecoin, dogecoin etc.) while others can be used as utility tokens, service tokens, finance tokens, etc. This makes them very heterogeneous and difficult to classify as their functions and applications continue to rise, thus making it challenging to be monitored by supervisory authorities (DeVries 2016; Sungit and Ahmad 2017; Adam 2017).

Classification of cryptocurrency

Crypto-currencies, also called digital currencies, refer to digital or virtual tokens that use cryptography to facilitate and record transactions on a set of electronic ledgersdatabases of financial accounts. Crypto-currencies have no tangible existence, rather they are electronic signals and records that keep track of transactions mediated with the currency (Smith and Kumar, 2018). They operate independently of a central bank or government. Coins live on their own blockchains. They can be used to purchase goods and services, or traded for other currencies, both digital and fiat. Digital cryptocurrencies refer to a form of exchange that only exist digitally and is not linked to any physical currency (Venter, 2016). The best known examples of popular cryptocurrencies include Bitcoin, Ethereum, and Litecoin. However, there are many other examples of digital cryptocurrencies at different stages of maturity on existence.

In the cryptocurrency industry, the terms "coin" and "token" are often used interchangeably, but they can have slightly different meanings.

A "coin" generally refers to a cryptocurrency that operates on its own blockchain. Bitcoin, Litecoin, and Bitcoin Cash are examples of coins. A "token" is a digital asset that is built on top of an existing blockchain. Tokens can represent an asset or utility, such as a digital asset that represents ownership in a company, or can be used to access a specific service or application.

Tokens are often issued through an Initial Coin Offering (ICO) or a Security Token Offering (STO). Thus, the main difference is that coins have their own blockchain and tokens don't.

A stablecoin is a type of cryptocurrency that is pegged to the value of a fiat currency, commodity or other cryptocurrency. The primary goal of a stablecoin is to reduce volatility and maintain a stable value compared to other cryptocurrencies, which can be highly volatile. This makes stablecoins more suitable for use as a medium of exchange or a store of value, like fiat currency.

The table 1 summarizes

Characteristics of cryptocurrency transactions

Cryptocurrencies are developed and held for several purposes, as a medium of exchange, similar to cash, but also for speculative purposes (short-term investment) and investment-like purposes (long-term appreciation value) (Venter, 2016). Given the lack of a government or central authority to support it, the survival of a cryptocurrency depends on market sentiment and investor confidence that this digital currency will become a widespread or more commonly used medium of exchange of the future. Conversely, it is this lack of government or central authority interference that gives a digital currency one of its benefits, a digital currency is fungible and transcends borders (Venter, 2016). For example, 1 bitcoin in Australia is the same 4 Since the crypto market is highly dynamic, the classification and ranking of cryptocurrencies can rapidly evolve based on technology evolution, market conditions and investors' reactions. Cryptocurrency transactions are decentralized, that is they are not controlled by any single entity such as a government or financial institution. Indeed, the blockchains distinguishing feature is its decentralised method. The network is protected by the proof-of-work protocol, doesn't need to entrust any intermediary to record and verify transactions [START_REF] Trivedi | Systematic Literature Review on Application of Blockchain Technology in E-Finance and Financial Services[END_REF].

Besides, there are some other features that make them interesting. Cryptocurrency is Digital in nature that makes that fast and easy to execute. The transactions can be in anonymous in nature so users do not have to provide personal information. They can be secured with advanced encryption techniques making them safe for users. Once the transaction is recorded on a block chain it cannot be altered or deleted. Some cryptocurrencies like Ethereum, allow for the creation of smart contracts, which are self-executing contracts with the terms of the agreement between buyer and seller being directly written into lines of code. All these features and characteristics make their adoption faster.

Business models around cryptocurrency

There are several different business models for individuals and entities that operate in the cryptocurrency space, such as crypto exchanges, mining, staking, payment processing, Initial

Coin Offering (ICO), cryptocurrency investment, lending and borrowing. We try to brief each model in next following paragraphs.

Crypto exchanges are platforms that allow users to buy, sell, and trade different  Hybrid Exchanges: These exchanges combine features of both CEX and DEX.

Examples include Binance DEX, and IDEX.

Risks associated with cryptocurrency

One of the biggest challenges in the financial reporting standard setting process is to identify risks associated with cryptocurrency that constantly evolve in the ecosystem and to ensure that those risks are fully reflected in the accounting treatment and disclosures in the financial statements. In the next following paragraphs, we highlight the main risks associated with investing in cryptocurrency.

The first and the most important one is volatility risk. Volatility risk is a significant concern of cryptocurrency transactions, as cryptocurrencies are known for their high degree of price fluctuation. The volatility of cryptocurrencies represents a significant challenge to investors, traders, and other users of cryptocurrencies, as it can lead to significant losses or revenue gains in a short period. One method of reducing the volatility risk is by incorporating stablecoins or pegged cryptocurrencies that are less volatile into the transaction process. Understanding volatility risk in cryptocurrency transactions is crucial for any investor or user of cryptocurrencies. By applying appropriate risk management strategies, investors can reduce the volatility risk and take advantage of the opportunities presented by this emerging asset class.

The second risk is cybersecurity. A cryptocurrency cannot be counterfeited due to the unique way in which the algorithm works that verify each transaction (Venter, 2016). However, cryptocurrency exchanges and wallets can be hacked or stolen, resulting in the loss of funds.

Additionally, phishing scams and other forms of fraud are common in the crypto space.

The third risk is associated with lack of regulation in cryptocurrency space. Cryptocurrency is not regulated by governments or financial institutions, making it more susceptible to fraud, hacking and other forms of financial crime.

The fourth risk is associated with foreign exchange risk; an entity may undergo that risk as soon as it wants to convert cryptocurrencies into legal currencies. The fifth risk is related to storage and transfer, if you lose access to your private key, you may permanently lose access to your cryptocurrency.

The last issue is related to smart contract risk. Smart contracts function with lines of code that run on blockchain, if there is a bug or vulnerability in the code, it could lead to a loss of funds.

While other risks are associated with liquidity, cryptocurrencies may not be as liquid as other investments and lack of understanding. Cryptocurrency is a relatively new and complex technology, and many investors may not fully understand how it works or the risks involved.

As companies increasingly use cryptocurrency as a medium of exchange or as an investment, they should consider how to capture, store, process, and organize data about cryptocurrencies in their accounting system; they should also consider financial risk exposure and impact on their performance [START_REF] Vincent | Accounting Research Opportunities for Cryptocurrencies[END_REF]. In order to close gaps in the regulation of crypto-assets, the EU sets up the Regulation MiCA (Markets in Crypto-Assets) by creating a common regulatory framework for the issuance of, intermediating and dealing in crypto-assets.

MiCA will introduce licensing and conduct of business requirements as well as a market abuse regime with respect to crypto-assets. Having given an overview of cryptocurrency ecosystem, in next section, we review the literature.

Accounting for crypto-assets: a literature review

Accounting research on crypto-assets seems to be in its infancy. Main accounting issues related to cryptocurrency can be categorized into discussions on asset definition, classification, accounting recognition and measurement, and disclosure requirements [START_REF] Vincent | Accounting Research Opportunities for Cryptocurrencies[END_REF][START_REF] Raiborn | Accounting issues related to Bitcoins[END_REF].

Definition of crypto-assets

In its Discussion Paper issued in July 2020, EFRAG raised a problematic of absence of legal or commonly accepted definition of the term "crypto-assets", and highlighted a pluralism in the use of related terminology due to the rapidly evolving ecosystem of products and application cases. A crypto-asset is therefore defined by EFRAG (2020) as "a digital representation of value or contractual rights created, transferred and stored on some type of distributed ledger technology (DLT) network (e.g. Blockchain) and authenticated through cryptography". In addition, "crypto-liabilities" are defined as "obligations that arise from the issuance of cryptoassets resulting in a present obligation for the issuing entity to transfer or grant access to an economic resource in digital or non-digital form".

In its agenda decision of June 2019, the IFRS Interpretation Committee (IFRS Foundation 2019) treats only holdings of cryptocurrencies and defines cryptocurrency as: (a) a digital or virtual currency recorded on a distributed ledger that uses cryptography for security; (b) not issued by a jurisdictional authority or other party; (c) does not give rise to a contract between the holder and another party.

In France, following the promulgation of the PACTE Law on May 2019, the Article L. 54-10-1 of the Monetary and Financial Code defines crypto-assets as "any digital representation of a value that is not issued or guaranteed by a central bank or by a public authority, which is not necessarily attached to a currency that has legal tender and which does not have the legal status of a currency, but which is accepted by individuals or organizations as a means of exchange, and which can be transferred, stored or exchanged electronically".

Classification and accounting recognition of crypto-assets

In order to properly account for crypto-assets, we must first answer the question of their classification. Are they part of the income statement or the balance sheet? In effect, there is a various number of terms used by market participants and stakeholders to designate crypto-assets and related activities: cryptocurrencies, crypto-tokens, digital tokens, DLT tokens, DLT assets, digital assets, virtual assets…Cryptocurrencies with no claim on the issuer are also interchangeably referred to as "crypto-coins", "payment tokens", "exchange tokens", "virtual currencies" or "payment-type crypto-assets".

As we observe that it is difficult to classify crypto-assets based on their heterogeneity at different levels. Therefore, the way in which these crypto-assets can be accounted for will have to take into account several elements. Should crypto-assets be classified by nature or function?

Is there an underlying asset in the transaction? Some crypto-assets give the right to an underlying good or service from an identifiable counterparty while other cryptocurrencies (e.g. bitcoin) do not give entitlement to an underlying good or service and have no identifiable counterparty. Furthermore, the accounting rules should encompass the different operations that can take place throughout the life of an active crypto-asset: creation, first issue and transactions on the secondary market. Another question is raised about the method of holding the cryptoassets. Indeed, while an entity can directly hold its crypto-assets in its own "portfolio", it is also possible that the crypto-assets of an entity are mixed in a common portfolio. By directly holding a crypto-asset in its own wallet, the entity has legal ownership of the crypto-asset. Therefore, recognition would depend on the rights and obligations related to how the crypto-assets are held.

As a result, one question arises whether cryptocurrencies are considered as a subset of cryptoassets. The EFRAG research (EFRAG Discussion Paper -July 2020) suggested that cryptocurrencies should be described as a subset of crypto-assets rather than synonym to cryptoassets. In this sense, crypto-assets include: (1) "cryptocurrencies" used as a means of payment;

(2) "utility tokens" that grant holders right to access network functionality or services; (3) "security tokens" that are assimilated to investments; (4) "stable coins" that are intended to mitigate the volatility of crypto-assets; and (5) "hybrid tokens" that combine different characteristics (e.g. tokens that have both utility and payment characteristics) (EFRAG 2020;

Cambridge Center for Alternative Finance 2019).

Another question arises whether an accounting standard setter should list all types of cryptoassets in order to define the appropriate accounting rules to each sub-set of those assets, or whether it should not tackle a particular category by proposing general accounting principles that encompass different characteristics and nature of crypto-assets. In the case of Bitcoin transactions, [START_REF] Tan | Bitcoin: Its Economics for Financial Reporting[END_REF] recommend the use of the concept of "substance over form"

to determine the applicable accounting treatment to make faithful representation. These authors conclude that knowledge of the underlying economics of the Bitcoin ecosystem is essential for accountants, and no new accounting standard is needed for financial reporting of Bitcoin.

Finally, it should be noted that crypto-assets are the first but not the only one case of blockchain technology. Accounting standard setters should be aware of the risk that existing or new accounting requirements applicable to crypto-assets may become insufficient or inappropriate for other extended applications of blockchain technology.

We suggest that a common vocabulary and a taxonomy of crypto investments should be developed and commonly applied by market participants including regulators, policymakers, accounting standard setters, holders and issuers of crypto-assets.

Nizam (2018) argued that digital assets require specific regulations in terms of recognition, measurement, and disclosure, and concluded that there are deficiencies in the IFRS for accounting of cryptocurrencies compared with the traditional IFRS framework. In addition, there are contradictory points of view on whether digital products should be recognized as intangible assets. According to Ajao & Theophius (2016), digital assets can be recognized as intangible assets if such items meet the definition and recognition criteria of intangible assets.

But regarding to [START_REF] Kang | Research on Accounting and Application of University Digital Assets[END_REF], digital assets are by no means equivalent to intangible assets because digital assets are not directly invested in production activities and cannot bring direct inflows of economic benefits. [START_REF] Fernandes | Defining issues: Blockchain and digital currencies challenge traditional accounting and reporting models[END_REF] argue that some digital assets, such as tokens or coins in an ICO, may convey specific utility of financial characteristics, such as rights to goods or services or a share of the profits of a project or business. In each case, issuers and holders of digital assets should carefully evaluate the specific characteristics of the asset to determine the appropriate accounting. Issuers would determine whether the token or coin should be accounted for in the financial statements as debt, equity, or a right to goods or services. The holders would determine whether it represents a financial asset, a right to goods or services or otherwise. For example, a token that confers specific rights to cash over time may meet the definition of a debt security or loan, whether or not ownership of the token is represented on a blockchain. EFRAG (2020) raised a number of issues related to the classification and the recognition of crypto-assets. On the one side, crypto-assets are characterized by relatively immature and opaque contracting arrangements, and this can make it difficult to precisely identify the underlying rights and obligations for some-crypto-assets, which in turn presents accounting challenges. On the other side, it can be difficult, even subjective to ascertain the business purpose for holding some utility and hybrid tokens as they have both investment and network functionality value attributes, then makes it difficult to achieve a consistent classification among companies based on business purpose. Consequently, there is still a lack of consensus as to how cryptocurrency should be classified in the balance sheet. [START_REF] Vincent | Accounting Research Opportunities for Cryptocurrencies[END_REF] suggest that researchers should thoroughly explore the classification that provides the most useful information to the users of financial statements, and the potential implications of misrepresenting cryptocurrency.

Accounting measurement of crypto-assets

If digital products are capitalized, their initial value and subsequent valuation basis should be determined. A digital product recognized as an asset should initially be measured at cost. The cost of the acquired digital product is the purchase price and the fair value would be appropriate for subsequent valuation of digital products. A fair value may be the market value or the net cash inflow into an entity expected from the use of the digital product. However, as the net cash inflow is a subjective measure, it would be more appropriate to use market value for the subsequent valuation of digital products [START_REF] Strader | Digital Product Management, Technology and Practice: Interdisciplinary Perspectives, Published in the United States of America by Business Science Reference[END_REF].

Where digital products are capitalized, depending on their accounting recognition as inventories or long-lived intangible assets, amortization and depreciation issues arise. If digital assets have an infinite life, they should not be amortized. In contrast, digital products with a finite life should be amortized over their useful life. For the purpose of amortization, the useful life of digital products should be determined. If digital products are classified as inventories, the lower of cost or net realizable value (which is the estimated selling price less the estimated costs of completion and sales) should be used for subsequent measurements (Mullins 2005).

Strader (2011) argued that the appropriate basis for measuring the value of digital assets is the fair value basis. IFRS 13 (para. 9) defines fair value as "the price that would be obtained when selling an asset or paid for a liability in an orderly transaction between market participants at a measurement date". The meaning of fair value includes both of entry price and exit price because it is closer to the reality of the situation when it is exchanged between dealers than between the seller and the buyer. Nevertheless, measurement in these markets makes fair value estimates based on self-management techniques; using fair value thus results in irrelevant and unreliable information for decision making as so as in higher costs associated with this value.

It is therefore argued that the obtained value will be unhelpful and conflict with the concept of information cost/utility for producing information. Another problem arises when the amount of income recognized under the fair value measurement is able to distort the real income due to the inclusion of unrealized gains or losses in the financial statements (Aladwan 2018).

By analysing financial statements of companies that have exposure to cryptocurrencies, Luo and Yu (2022) raise the inconsistency in accounting practices under GAAP and IFRS that can mislead users in accessing asset value, liquidity, profitability, and cash-generating abilities across firms. They observe that firms receiving cryptocurrencies in revenue-generating activities account for cryptocurrencies as intangibles using different measurement bases and classify the associated cash inflows differently. Some firms classify cryptocurrencies as longterm intangibles, while others consider them as liquid, short-term intangible assets.

Accounting disclosure of crypto-assets

A number of questions raise about financial disclosures of crypto-assets [START_REF] Vincent | Accounting Research Opportunities for Cryptocurrencies[END_REF]. Do investors value and expect information about cryptocurrency transactions to be disclosed on the financial statements, as a note to the financial statements, or in a separate section of the annual report? Whether and what type of information regarding cryptocurrency transactions should be disclosed in the financial statements? What is the best balance sheet presentation of cryptocurrencies that add value to the market? There are strong arguments to consider that crypto-assets should be properly disclosed in the financial report in accordance with the principle of materiality (EFRAG 2022). The valuation base, the amortization and the depreciation as so as the classification of the digital products should be clearly reported in the notes of the financial reports.

For companies providing both digital and traditionally-traded products, a segment reporting should be required to report any profit or loss resulting from digital products' operations. In addition, entities trading only digital products should also prepare segment reporting by regions, because trading of digital products is across borders [START_REF] Strader | Digital Product Management, Technology and Practice: Interdisciplinary Perspectives, Published in the United States of America by Business Science Reference[END_REF]. If the developed digital assets are replaced by better technology models, the value of those digital assets will be greatly reduced. Therefore, whether companies develop, invest and/or use cryptocurrency as an exchange medium, they should properly disclose significant risks associated with digital assets in the financial report [START_REF] Vincent | Accounting Research Opportunities for Cryptocurrencies[END_REF][START_REF] Kang | Research on Accounting and Application of University Digital Assets[END_REF].

Overview of accounting rules for crypto-assets

One of the main issues for the international accounting standard setting bodies such as the IASB and the FASB is to examine whether cryptocurrency is a pervasive issue. What are the entities that operate in the crypto ecosystem? What is the current and potential materiality of this issue?

What are the risks associated with cryptocurrency development and use? What is the impact of cryptocurrency on an entity's financial position and performance? Despite its increasing popularity, no official guidance on the financial reporting of Bitcoin transactions has been provided by standard setters [START_REF] Tan | Bitcoin: Its Economics for Financial Reporting[END_REF]. There are no specific accounting regulations for cryptocurrencies or crypto-assets at the global level. Furthermore, there is no consensus on how to account for crypto-assets at either company or country level.

At the international level, there is no specific IFRS dedicated to the accounting for cryptoassets. Nevertheless, in its agenda decision of June 2019, the IFRS Interpretation Committee (IFRS Foundation 2019) clarified that cryptocurrencies with no claim on the issuer should be classified as either intangible assets according to IAS 38 Intangible Assets or as inventories according to IAS 2 Inventories, depending on the purpose of holding the cryptocurrencies.

Facing national standard setters' initiatives to regulate accounting for cryptocurrency, the IASB defended its position in the regulatory space by issuing an agenda decision based on two existing standards [START_REF] Ramassa | Standard setting in times of technological change: accounting for cryptocurrency holdings[END_REF]. It should be noted that the IFRS IC decision in June 2019 did not cover neither the accounting by holders of other sub-sets of crypto-assets such as utility tokens and security tokens nor the accounting by issuers of crypto-assets. In fact, the IFRS IC did not consider cryptocurrency holding as a financial asset defined by IAS 32

Financial Instruments -Presentation. Cryptocurrency is not cash, but it can be a financial asset for security tokens that represent a residual interest in equity, or for stable coins that give holders an enforceable right to redeem the coins for cash (Luo and Yu 2022).

In the United States, neither the FASB nor the PCAOB have issued formal guidance for accounting and auditing cryptocurrency. The FASB issued a guidance in 2014 stating that cryptocurrency should be considered as an intangible asset and accounted for accordingly.

However, this guidance is not binding and individual companies may account for mine cryptocurrency or undertake initial coin or token offerings as well as the accounting for holding cryptocurrency as an intermediary or as an agent. Entities should comply with the disclosure requirements of the IFRS Standards they use in accounting for cryptocurrencies (e.g., IAS 2, IAS 38, IFRS 13). However, given the complexity and volatility associated with cryptocurrencies, entities should consider whether additional disclosures about their cryptocurrency holdings are necessary. In addition to the disclosures required by a specific IFRS Standard, the CPA Canada recommend specific disclosures in the notes to the financial statements, such as a description of the cryptocurrency, its important characteristics and the purpose of it; the number of units of the cryptocurrency held at year end; how the accounting policy was determined; if the cost model is used, the fair value for the cryptocurrency together with the appropriate IFRS 13 disclosures; and information on the market risk associated with the cryptocurrency.

In France, the national standard setter (Autorité des Normes Comptables: ANC) issued in December 2018 the Regulation ANC n° 2018-07 by laying down a structured accounting framework for holders and issuers of tokens. According to the ANC's approach, the accounting treatment of tokens issued is determined according to the rights and obligations attached to the tokens and described in the information documents made available to subscribers and holders while the method of accounting for the tokens held is based on the analysis of the intention to use the services associated with these tokens (Dao-Le Flécher 2019). Later on July 24 th 2020, the ANC issued the Regulation ANC n° 2020-05 that clarifies the accounting treatment for token lending and borrowing, token derivatives, as so as for digital asset service providers.

Nevertheless, the ANC seems to restrict its analysis to cryptocurrencies by using a general term "tokens" and assimilates the cryptocurrencies to existing categories of assets by proposing the existing accounting rules applicable to those assets.

In the UK, no accounting standard currently exists to explain how cryptocurrency should be accounted for, accountants should therefore refer to existing accounting standards (ACCA 2018).

The Accounting Standards Board of Japan (ASBJ) has worked on two questions, and within a restricted framework: (1) should the intermediary record assets and liabilities representative of the crypto-assets on which it operates; and (2) should he recognize as assets the crypto-assets he owns. The Board responded positively to both questions. The ASBJ issued lately in May 2022 a Discussion Paper on the accounting for issuance and holding of ICO tokens (ASBJ 2022). Nevertheless, there is no formal accounting framework for crypto-asset transactions in Japan.

The literature review enables us to make some preliminary conclusions. First, there is no specific international financial reporting standard dedicated to crypto transactions. Second, there is no formal accounting guidance for crypto-assets at the country level. Current GAAP and IFRS guidance fails to specifically address various aspects of crypto-assets that constantly evolve. In effect, there is no consensus on how to account for crypto-assets at company and country levels. Finally, there is no consensus on whether an accounting standard setter should propose a specific financial reporting framework dedicated to crypto transactions.

This overview of existing accountings rules leads us to raise the following debate. What are the explanations for the lack of convergence of financial reporting frameworks for crypto-assets?

While the international standard setters (IASB and FASB) as well as national accounting standard setters are active in monitoring the topic, they seem to adopt a standby position for the following reasons. First, the creation of a new accounting standard dedicated to crypto-assets risks to fail to reflect the economic substance of crypto transactions in an evolving ecosystem and to anticipate future developments in this area. Crypto-assets are the first but not the only one case of blockchain technology. Setting up accounting principles that encompass different characteristics and nature of crypto-assets represents a real accounting challenge for the international standard setters. Second, neither the IASB nor the FASB consider that cryptocurrency is a pervasive issue and that crypto transactions are material for listed companies. Third, given the evolving nature of crypto-assets and absence of materiality for listed companies, the international standard setters conclude that existing accounting standards are sufficient for companies to represent faithfully crypto transactions and to disclose them in the financial statements. Finally, the international standard setters prefer to elaborate a prudent strategy combining an active monitoring of the subject for knowledge building and being ready to set up a new accounting standard when the issue becomes pervasive for public listed companies.

Conclusion

In this research, we carry out a comparative study of accounting rules and practices relating to crypto-assets in Europe, US and Asia. We are in the process of conducting an analytical study of accounting practices in a sample of companies that develop, invest and/or use cryptocurrency as an exchange medium. Our study once achieved will be the first to our knowledge that focus on this topic with a large sample of companies from different countries and that examines the financial statements for the most recent reporting periods (2022 and 2021). Our preliminary results have several implications for future research work that would shed light on the building of a common set of accounting rules and principles related to cryptocurrency. Through proper financial reporting of cryptocurrencies, corporations can communicate to investors with risks associated with such volatile assets, market participants can assess their valuation implications, and government agencies can ascertain capital market consequences and tax effects.

  principal types of cryptocurrencies. The top trading cryptocurrencies identified by CoinGecko.com as of January 17 th 2023 are Bitcoin (BTC), Ethereum (ETH), Binance Coin (BNB), Dogecoin (DOGE), Cardano (ADA), XRP, Tether (USDT), Polkadot (DOT), Uniswap (UNI) et Litecoin (LTC) 4 .

  cryptocurrencies. They make money through transaction fees and sometimes by charging for additional services such as margin trading or staking. Some examples are like: Binance and Coinbase. Mining is the process of using powerful computers to validate transactions on the blockchain and earn rewards in the form of newly issued cryptocurrency. Companies that run mining operations can make money through the sale of the cryptocurrency they mine, as well as through the sale of the equipment and infrastructure used for mining. Staking is the process of holding a certain amount of cryptocurrency in a wallet to support the network and in return, the holder get rewards in form of newly issued cryptocurrency. Payment processing companies can provide services for merchants who want to accept cryptocurrency as payment and make money by charging fees for their services. Initial Coin Offering (ICO) is a type of fund raising campaign in which an entity issues a new cryptocurrency and sells it to investors in exchange for funding. Cryptocurrency investment is a business in which an entity pools funds from various investors and then invests them into different cryptocurrency assets, making money through capital appreciation and/or dividends. Blockchain consulting and development companies provide consulting and development services related to blockchain technology, such as building decentralized applications and smart contracts. They make money through consulting fees and by selling their products and services. Crypto lending and borrowing platforms enable users to lend and borrow cryptocurrencies and make money through interest charges.Thus, the main stakeholders in the cryptocurrency ecosystem include issuers and holders of cryptocurrencies, miners, developers of blockchain-based applications, exchange platforms, merchants who accept cryptocurrency as a form of payment, providers of digital wallets to store cryptocurrency, analysts, and consulting and legal services providers.It's worth noting that crypto exchange platforms play an important role in the crypto ecosystem by acting as a marketplace for the buying and selling of cryptocurrencies, and are similar to traditional stock exchanges. Cryptocurrency exchanges come in different forms and with different features, but most of them allow users to deposit funds, place orders to buy or sell, and execute trades. Some exchanges also offer margin trading and lending, which allow users to trade with leverage. there are several types of crypto exchanges:  Centralized Exchanges (CEX): These exchanges are operated by a central authority and act as an intermediary between buyers and sellers. Examples include Binance, Coinbase, and Kraken.  Decentralized Exchanges (DEX): These exchanges operate on a blockchain and use smart contracts to facilitate trades. They do not have a central authority and users remain in full control of their funds at all times. Examples include Uniswap, Kyber Network, and SushiSwap.

Table 1 : Classification of cryptocurrencies 5

 1

	Number	Types of cryptocurrencies
	1	Coins
	2	Tokens
	a)	Security Tokens
	b)	Utility Tokens
	c)	Payment Tokens
	d)	Non-Fungible Tokens
	e)	DeFi Tokens
	f)	Asset Backed Tokens
	g)	Privacy Tokens
	h)	Exchange Tokens
	i)	Meme Tokens
	j)	Governance Tokens
	k)	GameFi Tokens
	l)	Wrapped Tokens
	m)	Media and Entertainment Tokens
	3	Stablecoins
	a)	Fiat-Collateralized Stablecoins
	b)	Crypto-Collateralized Stablecoins
	c)	Algorithmic Stablecoins
	d)	Commodity-Backed Stablecoins

  1 bitcoin in Germany, is the same as 1 bitcoin in Argentina and so on. Unlike fiat money, a digital currency is not influenced by macroeconomic variables such as interest rates, GDP and fiscal policy(Ciain et al. 2016). It is worth noting that cryptocurrency transactions have a number of unique characteristics which stem from the blockchain technology and that set them apart from traditional financial transactions.

5

Source : https://corporatefinanceinstitute.com/resources/cryptocurrency/types-of-cryptocurrency/ and https://www.coingecko.com/learn/types-of-crypto accessed on January 17th 2023.

as

www.coingecko.com, accessed on January 17 th , 2023.

www.coingecko.com, accessed on January 17th, 2023.

cryptocurrencies in different ways. In the absence of formal accounting rules, the American Institute of Certified Public Accountants issued in 2020 non-binding guidance that cryptocurrency like Bitcoin should be accounted for as intangible assets, in accordance with ASC Topic 350 Intangibles -Goodwill and Other (AICPA 2020). Accordingly, for operating companies like Tesla and MicroStrategy, their holdings in Bitcoin are accounted for as intangible assets.

Given the ongoing evolution and the diversity of crypto-assets, on December 15 th 2021, the FASB added a project to its technical agenda to improve the accounting for and disclosure of certain crypto-assets. As a result, on December 14 th 2022, the Board decided to set up presentation requirements for all entities (FASB 2023). These requirements include: (1) presentation of the aggregate amount of crypto-assets separately from other intangible assets;

(2) presentation of gains and losses on crypto-assets in net income separately from those on other intangible assets; (3) classification of crypto-assets received as non-cash consideration during the ordinary course of business that are converted nearly immediately into cash as operating cash flows. Furthermore, the Board also decided to require an entity to disclose: (1) significant crypto-asset holdings (the name of the crypto-asset, fair value, units held, and cost basis); (2) a reconciliation of activity between the beginning and the end of the period for total crypto-asset holdings; (3) restricted crypto-assets (the fair value of the crypto-assets that are restricted from sale, the nature and remaining duration of the restriction).

In Canada, both the Canadian Accounting Standards Board (AcSB) and the Chartered Professional Accountants of Canada (CPA Canada) issued non-authoritative guidance stating that many cryptocurrencies are likely to meet the definition of intangible assets according to IAS 38 (AcSB 2019; CPA Canada 2018). Therefore, cryptocurrencies should be measured initially at cost, may be subsequently measured at either cost or at fair value in accordance with IFRS 13. The revaluation method can only be used if there is an active market for the cryptocurrency. Furthermore, cryptocurrencies that meet the definition of intangible assets and are held for sale in the normal course of business, should be accounted for in accordance with IAS 2. They would be measured at the lower of cost and net realizable value under the general inventory model required by IAS 2. As a result, decreases in net realizable value would be recorded in the statement of profit or loss while increases in net realizable value in excess of previously recorded decreases would not be recorded.

Nevertheless, this non-authoritative guidance only addresses the accounting for holdings of cryptocurrencies acquired from third parties, and excludes the accounting by entities which


A Hait
email: fhait@laas.fr

T Sim

M Ta

A Landmark-based Motion Planner for Rough Terrain Navigation

In this paper we describe a motion planner for a mobile robot on a natural terrain. This planner takes into account placement constraints of the robot on the terrain and landmark visibility. It is based on a two-step approach: during the rst step, a global graph of subgoals is generated in order to guide the robot through the landmark visibility regions; the second step consists in planning local trajectories between the subgoals, satisfying the robot placement constraints.

Introduction

Autonomous navigation on natural terrains is a complex and challenging problem with potential applications ranging from intervention robots in hazardous environments to planetary exploration. Mobility in outdoors environments has been demonstrated in several systems [START_REF] Simeon | A practical motion planner for all-terrain mobile robots[END_REF][START_REF] Hait | Motion planning on rough terrain for an articulated vehicle in presence of uncertainties[END_REF][START_REF] Hebert | Pixel-based range processing for autonomous driving[END_REF][START_REF] Ben Amar | Dynamic Analysis of O -Road Vehicles[END_REF].

The adaptive navigation approach currently developped at LAAS within the framework of the EDEN experiment 3] demonstrates fully autonomous navigation in a natural environment, gradually discovered by the robot. The approach combines various navigation modes (re ex, 2d and 3d) in order to adapt the robot behaviour to the complexity of the environment. The selection of the adequate mode is performed by a speci c planning level, the navigation planner 11] which reasons on a global qualitative representation of the terrain built from the data acquired by the robot's sensors.

In this paper, we concentrate on the motion planning algorithms required for the 3D navigation mode 13], selected by the navigation planner when very rugged terrain has to be crossed by the robot. On uneven or highly cluttered areas, the obstacle notion is closely linked with the constraints on the robot attitude, and therefore contrains the robot heading position. Planning a trajectory on such areas requires a detailed modeling of the terrain and also of the robot's locomotion system.

Several contributions recently addressed motion planning for a vehicle moving on a terrain [START_REF] Shiller | Optimal motion planning of autonomous vehicles in three dimensional terrains[END_REF][START_REF] Krotkov | Stereo Perception and Dead Reckoning for a Prototype Lunar Rover[END_REF][START_REF] Chatila | Planetary exploration by a mobile robot: mission teleprogramming and autonomous navigation[END_REF]2,[START_REF] Fillatreau | Modelling of unstructured terrain and feature extraction using b-spline surfaces[END_REF]. In particular, the geometric planner we proposed in [START_REF] Shiller | Optimal motion planning of autonomous vehicles in three dimensional terrains[END_REF][START_REF] Fillatreau | Modelling of unstructured terrain and feature extraction using b-spline surfaces[END_REF] is based on a discrete search technique operating in the (x; y; ) con guration space of the robot, and on the evaluation of elementary Figure 1. Placement of an articulated chassis feasible paths between two con gurations. The overall e ciency of the approach was made possible by the use of fast algorithms for placing the robot onto the terrain (Figure 1) and checking the validity of such placements.

In the navigation experiments previously conducted with a real robot 13], motion control was limited to executing the paths returned by this planner by relying on odometry and inertial data. The unpredictable and cumulative errors generated by these sensors, especially signi cant on uneven and slippery areas, often caused important deviations leading to a lack of robustness at execution. To overcome this problem, the robot has to be equipped with environment sensors (eg. cameras) that can provide additionnal information by identifying appropriate features of the terrain, and allow to use sensor-based motion commands. Such primitives are more tolerant to errors than classical position-controlled primitives, but their feasability has to be checked in term of visibility of the landmarks along the trajectory.

The contribution of this paper is to propose a motion planning approach which considers a set of given landmarks (eg. terrain peaks 5]) in the terrain model, and computes a partitionning of the terrain into regions where particular landmarks are visible. The approach allows to produce trajectories that remain, whenever possible, inside these visibility regions where the robot can navigate with respect to the given landmarks using closed-loop primitives relying onto the sensor's data.

The Motion Planning Approach

Problem statement

We consider a geometric model of an articulated robot illustrated by Figure 1. The robot is composed of several axles linked by passive joints allowing to adapt its shape to the terrain relief. The terrain is described by surface patches de ned from an elevation map in z associated with a regular grid in (x; y). The terrain model also contains a set of point landmarks corresponding to major terrain features that the robot should be able to track at execution. The robot motions are constrainted by: validity constraints related to the feasibility of the motion (eg. stability of the vehicle, collision avoidance with the terrain, mechanical constraints). visibility constraints which traduce the ability of the robot to detect one or a set of landmarks from a given con guration. While the rst constraints need to be veri ed to guarantee the safeness of the motion, it would be too restrictive to only consider solutions satisfying the visibility constraint all along the path. Therefore, the planning approach should generate solutions alternating large portions verifying the visibility of the landmarks (sensor-based mode), and subpaths where the landmarks cannot be used at execution (position-controlled mode).

A two-step approach

In order to separate the integration of the two kinds of constraints, we propose a motion planner based on the following two-step approach:

In the rst step, subgoals are generated in order to guide the robot through landmark visibility regions computed from the terrain model and the landmark set. These subgoals and the start/ nal con gurations are connected into a network of possible paths which minimize a cost re ecting the traversability of the terrain.

In the second step, a motion planner based on 6] is used to transform the possible paths into feasible ones verifying the validity constraints. The nal trajectory is a sequence of trajectories from a subgoal to another one, alternately in and out of the visibility regions. We describe below the two steps of the approach respectively called global planner and local planner.

The Global Planner

Landmark visibility

The landmarks de ne a partition of the terrain into regions, called the visibility regions, where particular landmarks are visible. Consider a robot equipped with an omnidirectional sensor. A landmark L i can be seen if the following constraints are respected: L i is not hidden by a part of the terrain. the distance from the sensor to L i is within some limit values.

For the rst constraint, we use a hierarchical model of the terrain (see 15]) that allows an e cient collision checking: if the segment connecting the sensor center to the landmark does not collide with the terrain, then the landmark can be seen from this position. The test is performed for every position respecting the second constraint and the set of points obtained is the visibility region of the landmark. For a given landmark L i , note that the visibility region may content several components. Each one is considered as a particular visibility region R ij .

Visibility graph

The visibility regions are then connected into a visibility graph. As illustrated by Figure 2, the graph has two type of edges. Some edges represent the possibility of a direct connection between two adjacent regions (ie. without crossing another region). These edges are rst computed by a numerical propagation technique described in the next section. This propagation, issued from the boundary of the visibility regions, allows to associate to the edges a path minimizing a cost evaluated from the terrain shape. The endpoints of these paths de ne the nodes of the graph. They correspond to a set of subgoals located onto the boundary of the visibility regions. The graph is then completed by additionnal edges connecting the di erent subgoals generated in the same visibility region. The paths associated to these edges are also computed by a numerical propagation performed inside the visibility regions.

The propagation algorithm

Let us now describe the propagation algorithm used to compute the visibility graph introduced in the previous section.

A cost bitmap is rst computed by evaluating for each point of the terrain model, the slope and the roughness of a circular domain centered at this position, with a radius related to the size of the robot. It represents the di culty for the robot to cross the domain.

The propagation consists in a wavefront expansion of a numerical potential obtained by integrating the cost across the bitmap, starting from each visibility region. The pixels belonging to the boundary of these regions are initialized to a null potential. At each iteration, the smallest potential pixel is expanded using an 8-neighbours propagation. Therefore, waves of increasing potential propagate from each region.

Whenever the waves issued from two regions meet together, an edge is created and the associated path is easily obtained by chaining back the pixels up to the associated region boundaries. The edge cost is the sum of the potentials computed at the meeting point. The propagation stops when all pixels have been expanded.

Path determination can take into account uncertainty growing outside the visibility regions by evaluating the maximum cost on a circular domain around the robot position, proportional to the uncertainty. This leads to a modi cation of the path that improve the robustness of the execution.

The Local Planner

The global planning step provides a sequence of subgoals between the initial and the goal con guration. The local planner is based on the algorithms described in 6]. Its role is to generate trajectories between the subgoals, while respecting the validity constraints (stability, non-collision, mechanical constraints).

The placement p = (q; r(q)) of the articulated robot (Figure 1) is dened by a con guration vector q = (x; y; ) specifying the horizontal position/heading, and by a vector r(q) of the joint parameters (the roll and pitch angles of the axles). For a given q, the values of r(q) depend on the contact relations between the wheels and the terrain. Computing the robot placement is required for the evaluation of the validity constraints considered by the planner.

Planning is performed in two steps: a preprocessing step to compute robot placements on the terrain, and the planning step itself.

Preprocessing step

The preprocessing step is aimed at reducing the computational cost of the robot placement. It consists in slicing the orientation parameter, and in computing for each slice, two surfaces that characterize the evolution of the roll angle and elevation of a single axle, in function of its position onto the terrain. This step has only to be performed once, before the rst call of the local planner.

Graph search

The planning step uses an approach similar to 1] in order to incrementally build a graph of discrete con gurations that can be reached from the initial position by applying sequences of discrete controls during a short time interval. The arcs of the graph correspond to feasible portions of trajectory, computed for a given control. Only the arcs verifying the validity constraints are considered during the search.

The heuristic function used to e ciently guide the search is based on the potential bitmap computed by the global planner. It also allows to follow, whenever possible, the paths computed at the global level.

Results and Discussion

The motion planning approach has been implemented in C on a Silicon graphics indigo workstation with an R4000 processor. We describe below some simulation results.For these examples, the terrain is represented by a 114 179 elevation map (see Fig 3).

Several steps of the global planner are shown on Figure 4: the cost bitmap and potential bitmap computed from the terrain model and three landmarks (Fig. 4-a The nal trajectory computed by the local planning step is displayed in Figure 5. One may note that a solution crossing the visibility regions computed for landmarks 3 and 1 would have been preferable for the visibility constraint. However, trajectories connecting the initial con guration to region 3 do not satisfy the validity constraints and the global planner had therefore to choose another path in the visiblity graph, leading to the nal trajectory shown on Figure 5. In the preprocessing step, data structures are computed from the terrain and the robot models: the cost bitmap, the hierarchical terrain model (quadtree) used by the collision checker and the orientation slices used by the local planner.

In the next example, only one landmark has been selected (Fig 6). The rst trajectory represents planning without landmarks 6]. The interest of the landmark-based approach is to allow the robot localisation in the landmark visibility region. Computation times are similar to the previous example.

The last example shows the in uence of uncertainty on path determination. Figure 7 represents cost bitmap for di erent uncertainty values. In Figure 8, taking into account uncertainty modi es the path by moving away from hazardous regions.

In the presented approach, the planned trajectories pass through the landmark visibility regions allowing robot localisation. Integrating uncertainty in cost bitmap is a rst step toward planning with uncertainty. This should be completed in a future work.

Experiment

We are currently working on the integration of the presented motion planner in the EDEN experimental testbed. Experiments will be performed with the LAMA Marsokhod (Figure 9) equipped with a range nder and a stereovision system for terrain modelling and landmark recognition. The purpose is to demonstrate autonomous navigation of a robot on rough terrain.

The robot is given a global goal in an unknown environement and perceives incrementaly the natural environment. At each step, a perception of a portion of the environment is done. This sensor information allows terrain modeling 13] and landmark extraction 5].

To use the landmark-based motion planner approach it is necessary to de ne a goal in the current perception. The goal position is chosen in order to ensure a good matching between the di erent perceptions.

At this level the landmark-based motion planner is called with this goal and landmark position. During the excution, landmark visual servoing is used inside the visibility regions, and classical odometry method outside these regions. After the path execution, a new step is done as far as the global goal is not reached.

Figure 2 .

 2 Figure 2. visibility regions and associated graph

Figure 3 .Figure 4 .

 34 Figure 3. The terrain model, the selected landmarks and the initial/ nal con gurations

Figure 6 .

 6 Figure 6. a-initial and goal con gurations b-trajectory without landmark ctrajectory with landmark

Figure 7 .Figure 8 .

 78 Figure 7. Cost bitmap with di erent uncertainty values

Figure 9 .

 9 Figure 9. The mobile robot Lama

Table 1 .

 1 Some computation times the gure. Computation times are reported in the following table.

	The nal trajectory
	time (sec.) cost bitmap quadtree slices Global planning visibility regions 0.500 Preprocessing 3.260 1.540 13.850 potential bitmap 2.470 visibility graph 0.930 Local planning graph searchs 2.000