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This paper addresses the control of steady state and transition behaviors for the bipedal spring-loaded inverted pendulum (SLIP) model. We present an event-driven control approach that enables the realization of active running, walking, and walk-run transitions in a unified framework. The synthesis of the controlled behaviors is illustrated by the notion of hybrid automaton in which different gaits are generated as the sequential composition of SLIP's primary phases of motion. We also propose a novel analytical approximate solution to the otherwise nonintegrable double-stance dynamics of the SLIP model. The analytical simplicity of the solution is utilized in the design and analysis of dynamic walking gaits suitable for online implementation. The accuracy of the approximate solution and its influence on the stability properties of the controlled system are carefully analyzed. Finally, we present two simulation examples. The first demonstrates the practicality of the proposed control strategy in creating human-like gaits and gait transitions. In the second example, we use the controlled SLIP as a planner for the control of a multibody bipedal robot model, and embed SLIP-like behaviors into a physics-based robot simulation model. The results corroborate both the practical utility and effectiveness of the proposed approach.
Shahbazi et al. (Fri,) studied this question.