Hybrid trajectory planning for a mechatronic tilting system

We discuss two trajectory design approaches for a mechatronic tilting system using a hybrid (discrete-continuous) modeling framework. Tilting means that the mechanical system under consideration rolls passively (unactuated) over one of its edges in contact with the environment. This occurs, for example, for walking machines when the foot tilts over its edge. Hybrid (discrete-continuous) system approaches have a great mechatronics application potential in the area of systems with (multiple) varying contacts between system and environment, e.g. walking systems, cars, hands, etc. The simple model system considered in this paper consists of an actuated arm, which is fixed on a base plate that can tilt over its edges. A mathematical model and two trajectory planning methods using a hybrid dynamical systems approach are proposed and the resulting trajectories are discussed in simulation. Some of the trajectories show sensitive parameter dependence, which is characteristic for chaotic systems.