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

arXiv: https://arxiv.org/abs/2205.09255 · HTML: https://mlsanity.com/paper/2205.09255/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2022.

## Built on by (most cited first, 6 of 6)

- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [Your Learned Constraint is Secretly a Backward Reachable Tube](https://mlsanity.com/paper/2501.15618/) (2025)
- [From Variance to Veracity: Unbundling and Mitigating Gradient Variance in Differentiable Bundle Adjustment Layers](https://mlsanity.com/paper/2406.07785/) (2024)
- [Shadow Program Inversion with Differentiable Planning: A Framework for Unified Robot Program Parameter and Trajectory Optimization](https://mlsanity.com/paper/2409.08678/) (2024)
- [Reinforcement Learning in a Safety-Embedded MDP with Trajectory Optimization](https://mlsanity.com/paper/2310.06903/) (2023)

## Abstract (arXiv)

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.