Abstract
Exploration vehicles, either manned or automatic, can use a variety of means of locomotion to achieve their goal. A first distinction must be made between ground vehicles, i.e. vehicles supported by a solid surface, atmospheric or sea vehicles, i.e. vehicles that move in a fluid without contact with the surface, be it a gas or a liquid, and space vehicles that move in the vacuum of space close to the surface. Most of this chapter is however devoted to the study of mobility on planetary surfaces, using different kind of supporting devices, like wheels or legs.
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Notes
- 1.
Perhaps the better known contributions to terramechanics are due to Bekker (e.g. M.G. Bekker, Theory of Land Locomotion, The University of Michigan Press, Ann Arbor, 1956; M.G. Bekker, Off-the Road Locomotion, The University of Michigan Press, Ann Arbor, 1960), who dealt also with the problem of ground locomotion on the lunar surface.
- 2.
The symbol μ ∗ is here used for the internal friction coefficient to avoid confusion with the traction coefficient μ defined later.
- 3.
K. Terzaghi, Theoretical Soil Mechanics, Wiley, New York, 1943; K. Terzaghi, R.B. Peck, G. Mesri, Soil Mechanics in Engineering Practice, Wiley, New York, 1996.
- 4.
D.P. Coduto, Geotechnical Engineering, Prentice Hall, Upper Saddle River, 1998.
- 5.
Ia.S. Ageikin, Off-the-Road Mobility of Automobiles, Balkema, Amsterdam, 1987.
- 6.
M.G. Bekker, Off the Road Locomotion, The Univ. of Michigan Press, Ann Arbor, 1960.
- 7.
V is the absolute velocity of the vehicle (or better, the velocity of the vehicle with respect to the ground, assumed as fixed), while V f is the relative velocity of the foot with respect to the vehicle. It is assumed to be positive when the foot moves backwards with respect to the body.
- 8.
J.Y. Wong, Theory of Ground Vehicles, Wiley, New York, 2001.
- 9.
Ia.S. Ageikin, Off-the-Road Mobility of Automobiles, Balkema, Amsterdam, 1987.
- 10.
G. Ishigami, A. Miwa, K. Nagatani, K. Yoshida, Terramechanics-Based Model for Steering Maneuver of Planetary Exploration Rovers on Loose Soil, Journal of Field Robotics, Vol. 24, No. 3, pp. 233–250, 2007.
- 11.
This definition, suggested by SAE, is different from that of (4.17), which in this case is
$$\sigma =\frac{R\varOmega -V}{R\varOmega }.$$The two formulations are essentially equivalent for small values of the slip.
Often they are both used for braking and driving, respectively:
$$\sigma =\frac{R\varOmega -V}{R\varOmega }\quad \mbox{for driving}\quad\mbox{and}\quad \sigma =\frac{R\varOmega -V}{V}\quad \mbox{for braking}.$$ - 12.
The slip velocity is defined by SAE Document J670 as Ω−Ω 0, i.e. the difference between the actual angular velocity and the angular velocity of a free rolling tire. Here a definition based on a linear velocity rather than an angular velocity is preferred: v=R e (Ω−Ω 0).
- 13.
Actually free rolling is characterized by a very small negative slip, corresponding to the rolling resistance. This is, however, usually neglected when plotting curves F x (σ).
- 14.
E. Bakker, L. Lidner, H.B. Pacejka, Tire Modelling for Use in Vehicle Dynamics Studies, SAE Paper 870421; E. Bakker, H.B. Pacejka, L. Lidner, A New Tire Model with an Application in Vehicle Dynamics Studies, SAE Paper 890087.
- 15.
Often the sign of the inclination angle is defined with reference to frame XYZ, while the sign of the camber angle depends on whether the wheel is at the right or left side of the vehicle. Here reference to frame XYZ will always be made.
- 16.
See, for instance, J.R. Ellis, Vehicle Dynamics, Business Books Ltd., London, 1969; G. Genta, Meccanica dell’autoveicolo, Levrotto & Bella, Torino, 1993. In the case of elastic non-pneumatic wheels such models may be more accurate than for pneumatic tires.
- 17.
As already stated, this definition is equivalent but not identical to that suggested by SAE. However, at the denominator both the velocity of the wheel V or the peripheral velocity ΩR can be used.
- 18.
G. Ishigami, A. Miwa, K. Nagatani, K. Yoshida, Terramechanics-Based Model for Steering Maneuver of Planetary Exploration Rovers on Loose Soil, Journal of Field Robotics, Vol. 24, No. 3, pp. 233–250, 2007.
- 19.
A. Azuma, The Biokinetics of Flying and Swimming, Springer, Tokyo, 1992.
- 20.
The Froude number can be also defined as \(\mathcal{F}_{r}=\frac{V^{2}}{gL}\), i.e. the square of that defined above. With this definition it can be interpreted as the ratio between inertial and gravitational forces.
- 21.
G.A. Cavagna, P.A. Willems, N.C. Heglund, Walking on Mars, Nature, Vol. 393, p. 636, June 1998; A.E. Minetti, Invariant Aspects of Human Locomotion in Different Gravitational Environments, Acta Astronautica, Vol. 39, No 3–10, pp. 191–198, 2001.
- 22.
D’Alembert, Traité de l’équilibre et du moment des fluides pour servir de suite un traité de dynamique, 1774.
- 23.
D’Alembert, Paradoxe proposé aux geometres sur la résistance des fluides, 1768.
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Genta, G. (2012). Mobility on Planetary Surfaces. In: Introduction to the Mechanics of Space Robots. Space Technology Library, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1796-1_4
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