FACTO: Function-space Adaptive Constrained Trajectory Optimization for Robotic Manipulators

A research team led by Yichang Feng, Xiao Liang, and Minghui Zheng has introduced FACTO (Function-space Adaptive Constrained Trajectory Optimization), a novel algorithm designed to improve motion planning for both single- and multi-arm robotic manipulators. Published on arXiv, the method represents a significant advancement in trajectory optimization by parameterizing robot movements as linear combinations of orthogonal basis functions and performing optimization directly in the coefficient space rather than traditional configuration space. This approach allows for more efficient handling of complex constraints and nonlinear dynamics that typically challenge robotic systems in real-world applications.

The technical innovation of FACTO lies in its dual approach: it combines a Gauss-Newton approximation with exponential moving averaging to smooth quadratic subproblems, while using coefficient-space mappings to address trajectory-wide constraints. The algorithm performs adaptive constrained updates via the Levenberg-Marquardt algorithm within the null space of active constraints. Experimental validation on Franka robots demonstrated that FACTO outperforms established optimization-based planners (CHOMP, TrajOpt, GPMP2) and sampling-based planners (RRT-Connect, RRT*, PRM) in both solution quality and feasibility, particularly in constrained multi-arm scenarios where coordination between multiple manipulators is essential. This advancement could accelerate deployment of more capable robotic systems in manufacturing, logistics, and healthcare settings.