CALIPSO: A Differentiable Solver for Trajectory Optimization with Conic and Complementarity Constraints

TL;DR

CALIPSO is a specialized differentiable solver for non-convex trajectory optimization in robotics, effectively handling complex constraints and enabling bi-level optimization, outperforming general-purpose solvers in challenging scenarios.

Contribution

It introduces CALIPSO, a novel differentiable solver that natively manages conic and complementarity constraints for trajectory optimization in robotics.

Findings

Successfully solves contact-implicit motion planning problems.

Demonstrates reliable convergence across manipulation, locomotion, and aerospace tasks.

Enables efficient bi-level optimization through solution differentiation.

Abstract

We present a new solver for non-convex trajectory optimization problems that is specialized for robotics applications. CALIPSO, or the Conic Augmented Lagrangian Interior-Point SOlver, combines several strategies for constrained numerical optimization to natively handle second-order cones and complementarity constraints. It reliably solves challenging motion-planning problems that include contact-implicit formulations of impacts and Coulomb friction and state-triggered constraints where general-purpose non-convex solvers like SNOPT and Ipopt fail to converge. Additionally, CALIPSO supports efficient differentiation of solutions with respect to problem data, enabling bi-level optimization applications like auto-tuning of feedback policies. Reliable convergence of the solver is demonstrated on a range of problems from manipulation, locomotion, and aerospace domains. An open-source implementation of this solver is available.