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.@en

This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.@en

This paper presents a coordination controller for the Dual-SLIP model, a novel template for quadrupedal steady and transitional running. The model consists of a pair of "physically-unconnected" Spring-Loaded Inverted Pendulums (SLIPs), each representing a part of the body of a quadruped (see Figure 1). For this model, we propose a spatiotemporal coordination controller that describes the evolution of coordination parameters by simple difference equations. A "time-aware" deadbeat low-level controller is also proposed to realizing the generated control specifications in each SLIP individually. Evaluation of the proposed coordination controller for the Dual-SLIP model in simulation shows that even with remarkably off-phase initial conditions and ground height variation disturbances, quadrupedal bounding, pronking and different transitions between them can be realized.

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