On modeling and locomotion of hybrid mechanical systems with impacts

Walking machines are mechanical systems that undergo impacts and changes in dynamic equations and can be viewed as a subclass of hybrid systems. In this work we focus on a class of planar mechanisms that can locomote through plastic impacts and clamping. This setting retains enough structure to investigate discrete phenomena in locomotion. We use a geometric framework to describe smooth phenomena such as inertial and constraint forces and discrete events such as impacts. In this setting hybrid mechanical control systems are described in terms of affine connections and linear jump transition maps. For this class of systems we perform a local controllability analysis. In particular we employ the notion of configuration controllability to identify systems that are able to locomote by clamping. Additionally, we discuss how to adapt smooth motion planning algorithms to this hybrid setting and present some instructive set of gaits.