Recursive Dynamics for Floating-Base Systems
Robotic systems studied in Chap. 6 have their bases fixed, however, in reality many robotic systems have their bases mobile or floating. In the case of a fixed-base robotic system, the base does not influence the dynamics, whereas it significantly influen
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Recursive Dynamics for Floating-Base Systems
Robotic systems studied in Chap. 6 have their bases fixed, however, in reality many robotic systems have their bases mobile or floating. In the case of a fixed-base robotic system, the base does not influence the dynamics, whereas it significantly influences the dynamics in the case of a floating-base robotic system. Space manipulators and legged robots are examples of floating-base robotic systems. Legged robots find applications in maintenance task of industrial plants, operations in dangerous and emergency environments, surveillance, maneuvering unknown terrains, human care, terrain adaptive vehicles and many more. In the case of legged robots they are either classified based on the number of legs, e.g., biped, quadruped, hexapod, etc., or the way it balances, e.g., statically or dynamically balanced. As reviewed in Chap. 2, legged robots (1) have variable topology, (2) move with high joint accelerations, (3) are dynamically not balanced if Center-of-Mass (COM) moves out of the polygon formed by the support feet, and (4) are under actuated. Hence, objective of achieving stable motion is difficult to decompose into actuator commands. Therefore, control of legged robots is intricate and dynamics plays vital role in achieving stable motion. As mentioned above, legged robots have variable topologies. One approach for their dynamic analyses is to have separate dynamic models for different topologies or configurations as shown by Shih et al. (1993), Raibert et al. (1993), Ono et al. (2001) and others. For example, when one foot of a biped is on the ground it can be treated as a fixed-base tree-type system, as analyzed in Chap. 6, whereas it is as a closed-loop system when both the feet are on the ground. Such configuration-dependant dynamic analysis is inconvenient when the system has many configurations, which are frequently changing as the robot walk. An alternative approach is to treat a biped or a quadruped as a floating-base system as proposed by Freeman and Orin (1991), Ouezdou et al. (1998) and Vukobratovic et al. (2007). In this approach, a foot touching the ground is a contact rather than fixed as in the configuration-dependant approach of Chap. 6. Hence, it may be referred to as the configuration-independent approach. The latter approach is more generic and helps in modeling legged robots in a unified manner, which is presented in this chapter. S.V. Shah et al., Dynamics of Tree-Type Robotic Systems, Intelligent Systems, Control and Automation: Science and Engineering 62, DOI 10.1007/978-94-007-5006-7 7, © Springer ScienceCBusiness Media Dordrecht 2013
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7 Recursive Dynamics for Floating-Base Systems
Contact problem for configuration-dependent approach is essentially to solve the kinematic constrains together with the equations of motion. In this approach, a single point contact is assumed and the contact remains fixed during the support phase, which is however not valid in reality. On the contrary, contact problem for configuration-independent approac
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