Discrete-input receding horizon control applied to pneumatic hopping robot energy regulation

In this work, a discrete input receding horizon controller (DIRHC) is proposed, as motivated by the need to use solenoid valves to control the motion of a pneumatic hoping robot. The proposed controller structure is for a switching control system in which only a finite number of discrete-valued control inputs are available. The controller utilizes a model to predict system behavior along a finite forward horizon, establishes an optimization problem, and finds the optimal control sequence of discrete-valued inputs. Stability is addressed by adding a terminal equality constraint to the control formulation. A modified depth first search algorithm, named sorted depth first search (sDFS), is presented to improve the searching efficiency and then compared to an exhaustive search. The proposed search preserves the completeness of the exhaustive search, while significantly reducing time and space complexity. The approach is applied to a pneumatic hopping robot system where the motion control is re-formulated as an explicit energy regulation problem. The proposed DIRHC controller and sDFS algorithm are used to realize the motion specification by maintaining the system energy around desired levels. Simulation results demonstrate the effectiveness of the proposed method.