Dynamics, stability, and actuation methods for powered compass gait walkers

In this paper, methods to achieve actively powered walking on level ground using a simple 2-dimensional walking model (compass-gait walker) are explored. The walker consists of 2 massless legs connected at the hip joint, a point mass at the hip, and an infinitesimal point mass at the feet. The walker is actuated either by applying equal joint torques at the hip and ankle, by an impulse applied at the toe off, immediately before the heel strike, or by the combination of both. It is shown that actuating the walker by equal joint torques at the hip and ankle on level ground is equivalent to the dynamics of the passive walker on a downhill slope. The gait cycle for the simplified walker model is determined analytically for a given initial stance angle. Stability of the gait cycle by an analytical approximation to the Jacobian of the walking map is calculated. The results indicate that the short-period cycle always has an unstable eigenvalue, whereas stability of the long-period cycle depends on selection of the initial stance angle. The effect of the torso mass by adding a third link attached at the hip joint is investigated. The torso link is kept in the vertical position by controlling the torque applied to it. The proportional-derivative control law is utilized to regulate the angular position error of the torso link. Using linearized dynamics for this walker, active control is applied to the ankle, which reduces the dynamics of the walker to the passive walker without the torso. The proposed walker is capable of producing stable walking while keeping the torso in an upright position.