Abstract
1. Introduction
The exploration of the planets and other bodies of our solar system is one of the most exciting aspects of 21st century science. Indeed, the recent emphasis placed on the search for life elsewhere in our solar system and beyond by a number of space agencies has made this venture of philosophical import. In particular, eyes have focussed on Mars, partly due to the astrobiological question of whether life might have existed there aeons past (Ellery, A., et al 2003), and partly due to the symbolic nature of this planet as a goal for human exploration in establishing a solid foundation for the subsequent colonisation of our solar system. The primary goal for a planetary rover is to navigate in an unknown, hostile terrain, recognise and negotiate obstacles, deploy scientific instrumentation and acquire samples from scientific targets. Surface planetary rovers are robotic vehicles that interact with hostile terrains and this interaction is the subject of this paper. Planetary rovers have a number of additional critical constraints that are generally absent from traditional terrestrial mobile robots:
adverse terrain characterised by rocks, cliffs, crevasses, etc with few features for self-localisation; lack of a priori data on the specific features of the environment to be explored; In this third of three short papers, I introduce some of the basic concepts of planetary rovers with an emphasis on some specific challenging areas of research that are peculiar to planetary robotics and not usually associated with terrestrial mobile robotics. The style of these short papers is pedagogical and this paper stresses the issue of rover-terrain interaction as an important consideration. Soil-vehicle interaction originates from military vehicle research but may be regarded as part of the dynamical approach to mobile robotics. For hostile planetary surfaces, this is essential in order to design a robotic rover with sufficient tractive capability to traverse planetary surfaces.
It is these issues that impose more stringent constraints on planetary rovers than are normally traditionally associated with terrestrial mobile robots, which have significant impact on the design and methodologies employed in planetary rovers. These techniques are currently being utilised for the design of the European ExoMars rover and a proposed European micro-rover (Vanguard) – see Fig. 1.
Proposed Vanguard micro-rover
2. The Primacy of the Environment
Most terrestrial mobile robotics platforms are operated in relatively benign environments such as office corridors and the like, despite recent emphasis on “embodied” or “situated” robotics paradigms which emphasise the necessity for dealing with realistic (and so uncompromising) environments (Clark, A., 1999). Planetary robotics does not have that luxury – planetary environments are rugged, hostile and a priori unknown. Indeed, for such applications, the environment and its characteristics are fundamental in determining robotic behaviour. The paradigm of situated robotics was initiated through behaviour-based robotics, which sought to emulate insect-level capabilities of locomotion and navigation without implementing specific planning or goal-handling (Brooks, R., 1986). The idea was to recapitulate the evolutionary process of incrementally increasing the sophistication of behavioural capabilities. A set of modular behaviours were implemented through a series of independent control layers, each of which was directly connected to sensors and actuators. Interaction between layers was minimised through the subsumption architecture, which suppressed the activity of competing behaviours. There was no symbolic representation of the environment as the real world itself was regarded as the agent's best world model. Brooks (1997) classified research into robot-environment interaction into six domain categories:
R0 – simulated robots without regard to physical dimensions or environmental location R1 – simulated robots calibrated by sensor-based world models R2 – as R1 but with the addition of stochastic noise R3 – simulated robots with simulated physics of sensors and actuators R4 – physical robot with sensors and actuators within the physical world
Despite protestations that real world environments are essential, much of situated robotics research has involved environments such as simple mazes that are no more “real” than traditional GOFAI (good old fashioned AI) environments symbolised by the “blocks world”. In some cases, office environments have been adopted, but even these environments are much simplified in comparison to natural terrains. Hence, to Brooks' classification, we would add two further categories:
R3b – simulated robots with simulated physics of sensors, actuators and environments R5 – physical robot with sensors and actuators within the physical world without simplification of that world.
For planetary robotics, simplified environments do not replicate the ruggedness and hostility of planetary environments. The mobility of the planetary rover directly determines the selection and value of scientific data and is therefore of primary importance to the space mission deploying such rovers. For these reasons, most emphasis in planetary robotics is with actuation capability and the issue of vehicle traction as components of robotic autonomy of primary importance, though autonomous navigation is also of importance, but is unlikely to be implemented on planetary rovers beyond behaviour control in the near future. This is not inconsistent with the situated robotics paradigm as action in the physical world takes precedence over all other activities such as sensory perception – the action component of the robot acts as a filter to sensory stimuli. Perception is continuously influences by the agent's activities and behaviour. Thus, actuation is fundamental to robotic behaviour and intelligence.
The dynamical perspective on robot-environment interaction has increased in importance in robotics. The agent and the environment may be viewed as two coupled dynamic systems characterised by their mutual interaction. Robot dynamics is in general non-Markovian in nature as future states are determined by both current and historical states – the reactive agent is a special case in that its behaviour is a function of its current state only. For this reason of determinism, reactive control only is preferred for the current generation of planetary rovers. The dynamic system is determined by a set of state variables and a dynamic law (typically in the form of a set of differential equations) that quantifies how those state variables change over time. The dynamics of the agent (A) and its environment (E) may be modelled as (Beer, R., 1995):
u=system dynamic parameters
These two dynamic systems are constantly coupled by their continuous interaction, which may be modelled by making the parameters of each system dependent on the state of the other system:
M=environment motor function of agent outputs dependent on the state of the agent
Coupling between these two systems occurs through feedback loops. The environment provides feedback whereby agent actions affect the environment, which determines the sensory input to the agent. The behaviour of an agent is a property of the coupled agent-environment interaction rather than the agent or the environment alone. Biologically, this requires the biological organism to fit the dynamic structure of its environment in order to survive, this adaptation being evolved by natural selection. Similarly, in artificial robots such as planetary rovers, the robot must dynamically fit its environment. As pointed out by Beer (1997), we traditionally carve up the physical universe into “agent(s)” and its “environment”. The agent dynamics may be divided into the agent's neural dynamics and body dynamics. Beer (1997) has used this principle to derive six-legged robotic gaits, which emerge as a result of the dynamic interactions of the environment (in this case, the “body” of the simulated arthropod and its control system). Although the entire physical universe cannot be modelled, nor is even relevant beyond local effects (thereby giving rise to the “frame” problem), I suggest that the “environment” should not be restricted to the body and its sensors and actuators but should include the wider, local environment. An important part of this wider environment includes the task required for the robot – the robot must have some specific function to be useful. The environment is uncertain, dynamically variable, unpredictable, and complex. Interaction with the agent is not limited to the sensory-motor system of the agent but to the physical agent as a whole, which includes the task characterisation, in this case traverse over the planetary terrain. The robot-environment interaction involves the dissipation of energy from the robot to the ground. It is this approach of modelling the energy transfer to the environment from the rover that we take here.
3. Martian Terrain
One important metric for determining the traversibility of planetary terrains is the mean free path which defines the straight-line distance that may be traversed before a steering change is required to avoid an obstacle. The shorter the MFP, the greater the demands and required sophistication of the autonomous navigation system. This is determined by the rock-size probability distribution on the planetary surface which for Mars may be modelled by (Golombek, M. & Rapp. D., 1997):
q=exponentiation coefficient
This enables computation of the MFP for any rock diameter D (Wilcox, B. et al 1997):
The rock size D0 is the maximum rock size negotiable by the rover which is determined by the design of the rover chassis. Evidently, increasing the negotiable rock size increases the mean free path – hence, the emphasis placed in planetary robotics on mobility systems, eg. the US rocker-bogie mechanism adopted for Sojourner and the Mars Exploration Rovers.
4. Bekker Theory
Bekker theory is used to model vehicle-terrain interactions (Bekker, M., 1969), particularly the behaviour of wheels, tracks and legs with different soil types. An important aspect of designing planetary rovers is tractive performance determined by soil mechanics. The vehicle traction metric is drawbar pull:
H = soil thrust determined by Mohr-Coulomb relation
R = total tractive resistance = Rc + ΔR A = ground contact area b= wheel/track width C0 = soil cohesion (clayey soils have high cohesion) φ = soil internal friction angle (sandy soils have high friction coefficient) s = soil vehicle slippage l = slippage distance κ = soil shear deformation modulus Rc = sinkage/compaction resistance
N=number of wheels k = kc + bkφ = soil sinkage deformation modulus kc = cohesion modulus of soil deformation kφ = friction modulus of soil deformation n = soil deformation exponent
= soil sinkage determined from Bernstein-Goriatchkin relation W = vehicle weight
The soil compaction (sinkage) resistance dominates over other sources of soil resistance, ΔR, such as bulldozing resistance. Some estimated values for the soil parameters are available from the Moon and Mars but planetary soil analogues can be used to determine estimates for unknown parameters. The greater the drawbar pull, the greater the tractive capability of the vehicle. Tracked vehicles offer much higher traction than wheeled vehicles by virtue of their greater ground contact area. Similar, the tractive advantage of grousers may be accommodated with Bekker theory. Bekker theory models may be calibrated with experimental data to provide the basis for low-level behaviour-control schema within an integrated autonomous navigation architecture utilising models of the form (Arkin, A., 1987; Iagnemma, K., Shibley, H., Dubowsky, S., 2002; Yoshida, K. et al 2002):
Such schema may provide the basis for traction-based reactivity to accommodate changes in soil characteristics and a degree of traction control through variable wheel torquing. The primary role for such a capability as part of an onboard autonomous navigation system is to provide for robust autonomous obstacle negotiation capability. This kind of robust locomotion as part of an autonomous navigation system is a pre-requisite for effective planetary rover missions given the limited scope for communication with such a remote robot.