This talk provides a survey of some recent applications of geometric mechanics and nonlinear control theory to problems in robotic locomotion and related areas. We also point out certain situations in which trajectory generation is particularly easy, allowing a dynamic motion planning problem to be reduced to a purely algebraic one. Simulations and videotape of experiments performed at Caltech will be used to illustrate the main ideas. The execution of such planned strategies may be assisted by guiding systems. Passive systems based on 6D localizers give information to the operator such that he can compare the planned task to the real one he executes.
Active systems are robots that realize part of the intervention autonomously.
Semi-active systems, more generally called synergistic systems, are based on the cooperation of a robotic device with a human operator. The basic principle of PADyC is to have a manually actuated arm that constrains the authorized motions of the surgical tool held by the human operator in function of a planned task. For instance, if the task is to stay inside a given 3D cartesian region, the motions of the tool will be free inside the region whilst some of them will be forbidden on the borders of this region. These constraints are realized by a patented mechanical system. The constraints are computed in the joint space from a cartesian description of the task.