Motion Planning for Mechanical Systems with Hybrid Dynamics

Planning and optimal control of mechanical systems are challenging tasks in robotics as well as in many other application areas, e.g. in automotive systems or in space mission design. This holds in particular for hybrid, i.e. mixed discrete and continuous dynamical models. In this contribution, we present an approach to solve control problems for hybrid dynamical systems by motion planning with motion primitives. These canonical motions either origin from inherent symmetry properties of the systems or they are controlled maneuvers that allow sequencing of several primitives. The motion primitives are collected in a motion planning library. A solution to a specific optimal control problem can then be found by searching for the optimal sequence of concatenated primitives. Energy efficiency often forms an important objective in control applications. We therefore extend the motion planning framework by primitives that are motions along invariant manifolds of the uncontrolled dynamics, e.g. trajectories on (un)stable manifolds of equilibria. The approach is illustrated by an academic example motivated by an operating scenario of an open-chain jointed robot.