A differential geometric approach to motion planning. (English) Zbl 0788.70017
Li, Zexiang (ed.) et al., Nonholonomic motion planning. Dordrecht: Kluwer Academic Publishers Group. Kluwer Int. Ser. Eng. Comput. Sci. 192, 235-270 (1992).
The motion planning problem for real analytic, controllable systems without drift is discussed, and a new strategy is proposed. A control that steers the given initial point to the desired target point is computed. A number of Lie brackets of the system vector fields are added. Formal calculations based on the product expansion relative to a Hall basis are used. The new control achieves the desired result on the formal level. This control provides an exact solution of the original problem.
For the entire collection see [Zbl 0875.00053].
For the entire collection see [Zbl 0875.00053].
Reviewer: J.V.Feitzinger (Bochum)
MSC:
| 70Q05 | Control of mechanical systems |
| 70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
