A hybrid model predictive controller for path planning and path following

The use of nonlinear model-predictive methods for path planning and following has the advantage of concurrently solving problems of obstacle avoidance, feasible trajectory selection, and trajectory following, while obeying constraints on control inputs and state values. However, such approaches are computationally intensive, and may not be guaranteed to return a result in bounded time when performing a non-convex optimization. This problem is an interesting application to cyber-physical systems due to their reliance on computation to carry out complex control. The computational burden can be addressed through model reduction, at a cost of potential (bounded) model error over the prediction horizon. In this paper we introduce a metric called uncontrollable divergence, and discuss how the selection of the model to use for the predictive controller can be addressed by evaluating this metric, which reveals the divergence between predicted and true states caused by return time and model mismatch. A map of uncontrollable divergence plotted over the state space gives the criterion to judge where reduced models can be tolerated when high update rate is preferred (e.g. at high speed and small steering angles), and where high-fidelity models are required to avoid obstacles or make tighter curves (e.g. at large steering angles). With this metric, we design a hybrid controller that switches at runtime between predictive controllers in which respective models are deployed.