Dual-Regularized Riccati Recursions for Interior-Point Optimal Control

Abstract-- We derive closed-form extensions of Riccati's recursions (both sequential [4] and parallel [7]) for solving dual-regularized LQR problems. We show how these methods can be used to solve general constrained, non-convex, discrete-time optimal control problems via a regularized interior point method, while guaranteeing that each primal step is a descent direction of an Augmented Barrier-Lagrangian merit function. We provide MIT -licensed implementations of our methods in C++ and JAX. Numerical optimal control, both real-time and offline, has found numerous application domains, ranging from trajectory optimization for robotics (e.g. for autonomous cars, unmanned aerial vehicles, legged robots) and airspace (e.g. Continuous-time optimal control problems, whose optimization variables are functions (thus infinite-dimensional) are typically converted into finite-dimensional optimization problems by either shooting (i.e.