Steering control of a hopping robot model during the flight phase

Two different types of steering control strategies for a hopping robot model during the flight phase are presented. The first strategy presents a time-varying feedback law based on the model reference approach, where the trajectory of the extended system is chosen as the model reference trajectory. The controllers are designed in such a way that after each time period the trajectory of the hopping robot model intersects the trajectory of the model reference, which can be made asymptotically stable. The second strategy presents discontinuous, state-dependent feedback control laws based on the construction of a cost function V which is the sum of two semi-positive definite functions V₁ (consists of the first m state variables which can be steered along the given vector fields) and V₂ (consists of the remaining n-m state variables which can be steered along the missing Lie brackets). The values of the functions V₁ and V₂ allow the determination of a desired direction of system motion and permit the construction of a sequence of controls such that the sum of these functions decreases in an average sense.