Optimal Control of an n-Legged Robot

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.