An Efficient Finite-Input Receding Horizon Control Method and Its Application for the Pneumatic Hopping Robot

In this paper, a finite-input receding horizon controller (FIRHC) is proposed as motivated by the need to use solenoid valves to control the motion of a pneumatic hoping robot. The controller aims to the application on switching control systems in which only a finite number of control inputs are available. The controller utilizes a model to predict system behavior along a finite forward horizon, and establishes an optimization problem, and then finds an optimal control sequence that gives the optimal cost and ultimately only the first element of the sequence is applied at each time step. The stability issue of the controller is discussed as a terminal equality constraint is added. Since only finite discrete inputs exist, the analytical solution is usually not possible to achieve, and exhaustive search was generally the approach to get the optimal control input. As is known, the exhaustive search becomes computationally prohibitive with an increasingly long horizon. An efficient modified depth first search algorithm is proposed, namely, sorted depth first search (sDFS). It preserves the completeness of exhaustive search, while significantly reducing time and space complexity. The whole approach is applied to a pneumatic hopping robot system where the motion control is re-formulated as an explicit energy regulation problem. The control goal is to maintain the system energy at a desired level. An additional example on a three tank control system is used to further illustrate the efficiency of sDFS method on the system with possession of a relatively large amount of modes. Simulation results demonstrate the effectiveness of the proposed method.