Trajectory generation for the unicycle model using semidefinite relaxations

European Journal of Control, vol. 80, pp. 101063

Abstract

We develop a convex relaxation for the minimum energy control problem of the well-known unicycle model in the form of a semidefinite program. Through polynomialization techniques, the infinite-dimensional optimal control problem is first reformulated as a non-convex, infinite-dimensional quadratic program which can be viewed as a trajectory generation problem. This problem is then discretized to arrive at a finite-dimensional, albeit, non-convex quadratically constrained quadratic program. By applying the moment relaxation method to this quadratic program, we obtain a hierarchy of semidefinite relaxations. We construct an approximate solution for the infinite-dimensional trajectory generation problem by solving the first- or second-order moment relaxation. A comprehensive simulation study provided in this paper suggests that the second-order moment relaxation is lossless.

Authors 4

1. Hannah Häring corresponding Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Chair of Intelligent Control Systems, RWTH Aachen University, D-52074 Aachen, Germany

2. Dennis Gramlich Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Chair of Intelligent Control Systems, RWTH Aachen University, D-52074 Aachen, Germany

3. Christian Ebenbauer Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Chair of Intelligent Control Systems, RWTH Aachen University, D-52074 Aachen, Germany

4. Carsten W. Scherer

   University of Stuttgart

   Affiliation as printed

   Chair of Mathematical Systems Theory, University of Stuttgart, 70569 Stuttgart, Germany