Increasing Computational Speed of Nonlinear Model Predictive Control Using Analytic Gradients of the Explicit Integration Scheme with Application to Collision Imminent Steering

In previous work, a collision imminent steering algorithm using nonlinear model predictive control (MPC) was developed for high speed applications where emergency maneuvers can bring the vehicle to its limits of handling. By exploiting the vehicle dynamics, the algorithm was shown in simulation to successfully perform a lane change maneuver in the shortest distance possible. However, it was unable to achieve realtime performance due to the computational expense in solving the underlying nonlinear optimization problem. To reduce the solution time, analytic derivatives of the trajectory simulation are derived in this paper, improving the gradient computation time and gradient accuracy. It is shown through examples that the analytic derivatives are an order of magnitude faster than finite differences, and the improved accuracy reduces the number of iterations required in the nonlinear gradient-based optimization by around 20%.