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Amortising Trajectory Optimisation for Residual MPC via Implicit Contact Differentiation

arXiv 2607.24959 ↗First posted 27 Jul 2026cs.RO cs.DC cs.LGcited by 0

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Abstract (arXiv)

Differentiable simulation can accelerate contact-rich trajectory optimisation by exposing local sensitivities of task outcomes to controls. Existing approaches either use finite differences, which are expensive and step-size sensitive; differentiate iterative contact solvers by unrolling automatic differentiation (AD), which stores a growing computation trace; or require intricate, solver-specific KKT sensitivity derivations. We introduce an AD-assisted implicit derivative for regularised smooth contacts and apply it to Mujoco MJX, based on the Implicit Function Theorem (IFT). The method differentiates the stationarity residual at the tolerance-converged solution, avoiding both solver unrolling and hand-assembled KKT systems. IFT keeps compiled temporary memory nearly constant with solver effort, changing by less than 4% from one to ten iterations versus 10.6× growth for unrolled AD. IFT memory grows slower with active contacts and model dimension, using 20× less memory at 256 contacts and 6× less at 16 contacts and 96 DoF. We further introduce optimiser distillation for residual MPC, amortising batched full-horizon iLQR into a policy that guides short-horizon residual iLQR. Across Finger, Franka, and Unitree, this raises six-step success by 28-98 percentage points over standard iLQR.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 42 references that are in the map. First posted on arXiv 27 Jul 2026.

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31 of 42 references.

References · 31

  1. 2015End-to-End Training of Deep Visuomotor Policiescited by 847
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  3. 2023TD-MPC2: Scalable, Robust World Models for Continuous Controlcited by 482
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19 more
  1. 2020Scalable Differentiable Physics for Learning and Controlcited by 72
  2. 2021Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contactcited by 50
  3. 2019Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Controlcited by 29
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  5. 2019Large Scale Model Predictive Control with Neural Networks and Primal Active Setscited by 28
  6. 2016PLATO: Policy Learning using Adaptive Trajectory Optimizationcited by 23
  7. 2021Differentiable Implicit Soft-Body Physicscited by 9
  8. 2025Dexterous Contact-Rich Manipulation via the Contact Trust Regioncited by 8
  9. 2022Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?cited by 6
  10. 2023Contact Models in Robotics: a Comparative Analysiscited by 6
  11. 2025Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robotscited by 6
  12. 2023Improving Gradient Computation for Differentiable Physics Simulation with Contactscited by 5
  13. 2024Contact-Implicit Model Predictive Control for Dexterous In-hand Manipulation: A Long-Horizon and Robust Approachcited by 5
  14. 2024Highly-Efficient Differentiable Simulation for Roboticscited by 5
  15. 2025Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Controlcited by 5
  16. 2025Whole-Body Model-Predictive Control of Legged Robots with MuJoCocited by 3
  17. 2025GATO: GPU-Accelerated and Batched Trajectory Optimization for Scalable Edge Model Predictive Controlcited by 2
  18. 2021GPU Accelerated Batch Multi-Convex Trajectory Optimization for a Rectangular Holonomic Mobile Robotcited by 1
  19. 2022Contact-Implicit Trajectory Optimization with Hydroelastic Contact and iLQRcited by 1

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