The problem of determining energy optimal walking motions for a bipedal walking robot is considered. A full dynamic model of a planar seven-link biped with feet is derived including the effects of impact of the feet with the ground. Motions of the hip and feet during a regular step are then modelled by 3rd order polynomials, the coefficients of which are obtained by numerically minimising an energy cost function. Results are given in the form of walking profiles and energy curves for the specific cases of motion over level ground, motion up and down an incline, and varying payload.

This paper presents a method for optimizing the walking motions of a planar five-link biped. The technique starts with non-linear kinematic and dynamic models for both the single-support and impact stages of motion. A variational technique is then used to derive joint trajectories that minimize a simple cost function. The resulting two-point boundary value problem is solved using a finite difference technique, with trajectories obtained from a simple linearized model as initial conditions. Families of optimal trajectories for different step periods and step lengths are presented.

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This paper presents a method for controlling the dynamic balance of legged robots using optimal state feedback. Rather than being restricted to a specific number of legs, the method considers the general case of a machine with n legs. The analysis starts with a non-linear dynamic model of a general robot and a set of equations representing the constraints on motion imposed by those feet in contact with the ground. These equations are used to derive a state-space model of order proportional to the number of degrees of freedom of the system, which will vary with the current constraint conditions. An optimal feedback gain matrix is then calculated for the linear model using standard techniques. The choice of operating point and optimization parameters is discussed. The effectiveness of the method is illustrated through simulation responses obtained .for a biped model under both single and double support constraint conditions.

Steady state errors resulting from gravitational loading are significant in legged robots, particularly when controller gains are set to low values to achieve the desirable property of compliant legs. This paper presents a gravity compensation scheme which not only eliminates steady state errors but which also generates foot reaction distributions that are optimal in terms of minimizing the likelihood of foot constraints being broken. This is achieved by minimizing a cost function, designed to reflect the condition of foot constraints, in conjunction with the equations of static equilibrium for the robot. A method of performing the minimization based on a combination of an analytical and a Newton—Raphson technique is presented. Results are given for hexapod and biped simulation models and for an experimental biped.