Model Predictive Control for Underwater Robots in Ocean Waves

Underwater robots beneath ocean waves can benefit from feedforward control to reduce position error. This paper proposes a method using Model Predictive Control (MPC) to predict and counteract future disturbances from an ocean wave field. The MPC state estimator employs a Linear Wave Theory (LWT) solver to approximate the component fluid dynamics under a wave field. Wave data from deployed ocean buoys is used to construct the simulated wave field. The MPC state estimator is used to optimize a set of control actions by gradient descent along a prediction horizon. The optimized control input minimizes a global cost function, the squared distance from the target state. The robot then carries out the optimized trajectory with an emphasis on real-time execution. Several prediction horizons are compared, with a horizon of 0.8 seconds selected as having a good balance of low error and fast computation. The controller with the chosen prediction horizon is simulated and found to show a 74% reduction in position error over traditional feedback control. Additional simulations are run where the MPC takes in noisy measurements of the wave field parameters. The MPC algorithm is shown to be resistant to sensor noise, showing a mean position error 44% lower than the noise-free feedback control case.