Nonlinear Probabilistic Model Predictive Control Design for Obstacle Avoiding Uncrewed Surface Vehicles

The primary objective of this research is to develop a probabilistic nonlinear model predictive control structure (NMPC) that efficiently operates uncrewed surface vehicles (USVs) in an environment that has probabilistic disturbances, such as wind, waves, and currents of the water, while simultaneously maneuvering the vehicle in a way that avoids stationary or moving stochastic obstacles in its path. The proposed controller structure considers the mean and covariances of the inputs or state variables of the vehicle in the cost function to handle probabilistic disturbances, where an extended Kalman filter (EKF) is utilized to calculate the mean, and the covariances are calculated dynamically via a linear matrix equality based on this mean and obtained system matrices with successive linearization for every sampling instance. The proposed control structure deals with non-zero-mean probabilistic disturbances such as water current via an innovative approach that treats the mean of the disturbance as a deterministic part, which is estimated by a disturbance observer and eliminated by a control term in the controller in addition to the control signal obtained via MPC optimization; the effect of the remaining zero-mean part is handled over its covariance during the probabilistic MPC optimization. The probabilistic constraints are also dealt with by converting them to deterministic constraints, as in linear probabilistic MPC. However, unlike the linear MPC, these constraints updated each sampling instance with the information obtained via successive linearization. The control structure incorporates the velocity obstacle (VO) method for collision avoidance. In order to ensure stability, the proposed NMPC adopts a dual-mode strategy, and a stability analysis is presented. In the second mode, an LQG design that ensures stability in the existence of non-zero mean disturbance is also provided. The simulation results demonstrate that the proposed probabilistic NMPC framework effectively handles probabilistic disturbances as well as both stationary and moving obstacles, ensuring collision avoidance while reaching the desired position and orientation through optimal path tracking, outperforming the conventional NMPC.