Vladimir M. Zakalyukin

Motion Planning and Fastly Oscillating Controls

We consider the motion planning problem, where the nonholonomic constraints are given by a strong-bracket-generating distribution. Approximating a nonadmissible trajectory by an admissible one in the sub-Riemannian setting, we prove a theorem which provides an exact asymptotic estimate of the “interpolation entropy” in the case of a free nilpotent algebra of first brackets. This theorem shows that we can approximate in an asymptotically optimal way using sinusoidal fastly oscillating controls. In the general case we obtain similar results; however, the estimates are less explicit.

Nonholonomic Interpolation for Kinematic Problems, Entropy and Complexity

Here we present the main lines of a theory we developed in a series of previous papers, about the motion planning problem in robotics. We illustrate the theory with a few academic examples.