Real-Time Simultaneous Optimistic Planning for Hybrid-Input Nonlinear Optimal Control

Simultaneous Optimistic Planning for Hybrid-Input Systems (SOPHIS) is a powerful method for the near-optimal control of nonlinear systems with hybrid - continuous and discrete - inputs, which works by iteratively splitting sets of input sequences. The generality of SOPHIS however comes at high computational costs that are often untenable in real-time control, especially for fast unstable systems. We introduce two modifications that make SOPHIS more suitable for real-time control: running it on a separate machine, over multiple sampling periods, while applying several inputs to the system during this time; and parallelizing the algorithm by splitting several sets simultaneously across multiple threads. Experiments investigate two parallelization schemes, the impact of thread count on the execution time, and the influence of the prediction horizon and budget; the latter on a real-life fast unstable system, a rotary inverted pendulum. In the experiments, the discrete input controls the quantization accuracy of the control action sent to the system.