This paper investigates the energetic effects of adding springs at the passive ankles of a planar five-link, four-actuator walking biped robot. The energetic cost of walking with springs was determined by using a walking motion designed for the biped without springs added. The walking motion was then optimized for the presence of springs of various arbitrarily chosen stiffnesses and offset angles. The stability properties of the motions that resulted were checked. The energetic costs of walking and standing were then computed. It was found that standing with springs was more efficient, while walking was more costly than the same action without springs. Finally, the spring characteristics (stiffness and offset angle) and the motion were optimized simultaneously. The costs for walking and standing were computed, revealing that walking with springs was more efficient and standing was more costly than doing either without springs. A methodical approach to choosing the size of the feet based on this analysis of the spring characteristics is also presented.

This paper presents a method of integrating kinematic mechanism design and hybrid system analysis for the design of a single-degree-of-freedom (DOF) planar biped robot that can achieve dynamic walking gaits that are stable. Reducing the DOF in a biped can result in a reduction of the complexity of the control strategies needed to enable stable walking. Although the biped designed by this procedure is restricted to a single gait, this biped may be less complex, lighter, and less costly to construct than one whose multiple DOF are coordinated via feedback.

This paper presents a new definition of stable walking - that is not necessarily periodic - for a class of biped robots. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a model of a 5-link biped.

This paper presents the experimental implementation and validation of a framework for the systematic design, analysis, and performance enhancement of controllers that induce stable walking in N-link underactuated planar biped robots. Controllers designed via this framework act by enforcing virtual constraints - holonomic constraints imposed via feedback - on the robot's configuration. The stability properties of the resulting walking motions may be easily analyzed in terms of a two-dimensional sub-dynamic of the full walking model. The experimental validation is performed on RABBIT, a 5-link prototype constructed by the French project Commande de Robots a Pattes of the CNRS-GdR Automatique.

The primary goal of this paper is to demonstrate a means to prove asymptotically stable walking in an underactuated, planar, five-link biped robot model. The analysis assumes a rigid contact model when the swing leg impacts the ground and an instantaneous double support phase. The specific robot model analyzed corresponds to a prototype under development by the Centre National de la Recherche Scientifique (CNRS), Paris, France. A secondary goal of the paper is to establish the viability of the theoretically motivated control law. This is explored in a number of ways. First, it is shown how known time trajectories, such as those determined on the basis of walking with minimal energy consumption, can be incorporated into the proposed controller structure. Secondly, various perturbations to the walking motion are introduced to verify disturbance rejection capability. Finally, the controller is demonstrated on a detailed simulator for the prototype which includes torque limits and a compliant model of the walking surface, and thus a noninstantaneous double support phase.

Closed-loop, asymptotically stable walking motions are designed for a 5-link, planar bipedal robot model with one degree of underactuation. Parameter optimization is applied to the hybrid zero dynamics, a 1-DOF invariant subdynamics of the full robot model, in order to create asymptotically stable orbits. Tuning the dynamics of this 1-DOF subsystem via optimization is interesting because asymptotically stable orbits of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The optimization process uses a sequential quadratic programming (SQP) algorithm and is able to satisfy kinematic and dynamic constraints while approximately minimizing energy consumption and ensuring stability. This is in contrast with traditional approaches to the design of walking controllers where approximately optimal walking (time-) trajectories are derived and then enforced on the robot using a trajectory tracking controller.