Maneuver-based motion planning for nonlinear systems with symmetries

TLDR

The paper proposes an efficient solution for motion‑planning problems in time‑invariant dynamical control systems with symmetries, such as mobile robots and autonomous vehicles, under various differential and algebraic constraints. The method represents motion plans as concatenations of primitives from a finite library, with concatenation rules encoded as a regular language via a Maneuver Automaton, and provides reachability analysis and algorithms for solving motion‑planning problems. The approach reduces steering problems for nonlinear systems with symmetries and invariant constraints to a sequence of kinematic inversion problems, and is illustrated on a small aerobatic helicopter.

Abstract

In this paper, we introduce an approach for the efficient solution of motion-planning problems for time-invariant dynamical control systems with symmetries, such as mobile robots and autonomous vehicles, under a variety of differential and algebraic constraints on the state and on the control inputs. Motion plans are described as the concatenation of a number of well-defined motion primitives, selected from a finite library. Rules for the concatenation of primitives are given in the form of a regular language, defined through a finite-state machine called a Maneuver Automaton. We analyze the reachability properties of the language, and present algorithms for the solution of a class of motion-planning problems. In particular, it is shown that the solution of steering problems for nonlinear dynamical systems with symmetries and invariant constraints can be reduced to the solution of a sequence of kinematic inversion problems. A detailed example of the application of the proposed approach to motion planning for a small aerobatic helicopter is presented.