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Indeterminate multi-point impact with friction of agile legged robots

This work presents an analysis of the simultaneous, multiple point impact forces on an agile legged robot. An analytic solution is developed for determining the system's post impact dynamic behavior. A discrete, algebraic model is used with an event-driven function which finds impact events. The indeterminate nature of the system equations of motion encountered at impact is addressed with the implementation of a constraint equation. An algorithm that is based on an analytic approach and an energetic COR is used to resolve the post impact velocities of the system. A simple planar model of a ball is considered for the leg's foot and a simulation is presented to demonstrate the effectiveness of the proposed approach.