Safe Optimal Control using Log Barrier Constrained iLQR

TL;DR

This paper introduces a novel constrained iLQR method that uses log barrier functions to effectively handle box constraints in nonlinear optimal control, improving stability and ensuring constraint satisfaction.

Contribution

The paper develops a smooth interior-point iLQR framework with log barrier functions, enhancing numerical stability and preserving convexity in constrained nonlinear control problems.

Findings

Reliable constraint satisfaction demonstrated in numerical examples

Enhanced numerical stability and convergence due to positive definite Hessians

Feedback gains naturally diminish near constraint boundaries

Abstract

This paper presents a constrained iterative Linear Quadratic Regulator (iLQR) framework for nonlinear optimal control problems with box constraints on both states and control inputs. We incorporate logarithmic barrier functions into the stage cost to enforce box constraints (upper and lower bounds on variables), yielding a smooth interior-point formulation that integrates seamlessly with the standard iLQR backward-forward pass. The Hessian contributions from the log barriers are positive definite, preserving and enhancing the positive definiteness of the quadratic approximations in iLQR and providing an intrinsic regularization effect that improves numerical stability and convergence. Moreover, since the negative logarithm is convex, the addition of log barrier terms preserves convexity if the cost is already convex. We further analyze how the barrier-augmented iLQR naturally adapts feedback gains near constraint boundaries. In particular, at convergence, the feedback terms associated with saturated control channels go to zero, recovering a purely feedforward behavior whenever control is saturated. Numerical examples on constrained nonlinear control problems demonstrate that the proposed method reliably respects box constraints and maintains favorable convergence properties.