2024 Volume 15 Issue 4 Pages 920-937
This paper discusses discretization methods for implementing nonlinear model predictive controllers using Iterative Linear Quadratic Regulator (ILQR). Finite-difference approximations are mostly used to derive a discrete-time state equation from the original continuous-time model. However, the timestep of the discretization is sometimes restricted to be small to suppress the approximation error. In this paper, we propose to use the variational equation for deriving linearizations of the discretized system required in ILQR algorithms, which allows accurate computation regardless of the timestep. The use of the variational equation with a longer timestep can improve control performance, in terms of the optimality of the trajectory and the robustness to measurement noises, by increasing the number of ILQR iterations possible at each timestep in the real-time computation. Case studies of the swing-up control of an inverted pendulum on a cart and a rotary inverted pendulum are provided to demonstrate the effectiveness of the proposed method.