Abstract
We investigate an inverse optimal control problem in which both some inequality constraints and the weights of a linear combination of cost terms are unknown. To understand the locally optimal behavior of the observed trajectories under these unknown parameters, we employ the Karush-Kuhn-Tucker (KKT) conditions. However, enforcing KKT conditions for both constraints and objective weights simultaneously introduces bilinear couplings, making the problem difficult to solve directly. To enhance tractability, we approximate the unknown inequality constraints with a convex hull to relax bilinear form. Given approximate constraints, we minimize the L2 norm of the stationarity and complementary slackness correcting deviations stemming from the convex hull approximation, to recover objective function from locally-optimal demonstrations. We validate our approach on a 2-DOF robotic arm, explicitly testing its performance with noisy data. Numerical results show that our method reliably recovers both the constraint set and objective-weight parameters under noise perturbations and supports effective planning of new constraint-satisfying trajectories in robotic control applications.
