Complexity of control-affine motion planning

Abstract

In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities.

28 pages, 5 figures

References in corpus (3)

• Approximate controllability, exact controllability, and conical eigenvalue intersections for quantum mechanical systems
• Resonance of Minimizers for $n$-level Quantum Systems with an Arbitrary Cost
• Hölder equivalence of the value function for control-affine systems

Cited by in corpus (1)

• On exponential stabilization of nonholonomic systems with time-varying drift