New IFT method cuts robot trajectory memory 20x, boosts success 98%

A team led by Daniel Layeghi and colleagues has introduced a novel method for amortising trajectory optimisation in contact-rich robotic control. Their approach leverages an automatic differentiation (AD)-assisted implicit derivative for regularised smooth contacts, based on the Implicit Function Theorem (IFT) and implemented in Mujoco MJX. Unlike existing techniques that either rely on expensive finite differences or unroll iterative solvers (which grow computation traces), the IFT method differentiates only the stationarity residual at the tolerance-converged solution. This avoids both solver unrolling and hand-assembled KKT systems, dramatically reducing memory overhead.

In benchmarks, IFT compiled temporary memory grew less than 4% when increasing solver iterations from one to ten, compared to 10.6x growth for unrolled AD. At 256 active contacts, IFT used 20x less memory; at 16 contacts with 96 degrees of freedom, it used 6x less. The team further introduces optimiser distillation for residual model predictive control (MPC), where a policy learned from batch full-horizon iLQR guides a short-horizon residual iLQR. Across three robotic platforms—Finger, Franka, and Unitree—this distillation raised six-step task success by 28 to 98 percentage points over standard iLQR, demonstrating both memory efficiency and practical control improvements.