DRAFTO: Decoupled Reduced-space and Adaptive Feasibility-repair Trajectory Optimization for Robotic Manipulators

This paper introduces Function-space Adaptive Constrained Trajectory Optimization (FACTO), a new trajectory optimization algorithm for both single- and multi-arm manipulators. Trajectory representations are parameterized as linear combinations of orthogonal basis functions, and optimization is performed directly in the coefficient space. The constrained problem formulation consists of both an objective functional and a finite-dimensional objective defined over truncated coefficients. To address nonlinearity, FACTO uses a Gauss-Newton approximation with exponential moving averaging, yielding a smoothed quadratic subproblem. Trajectory-wide constraints are addressed using coefficient-space mappings, and an adaptive constrained update using the Levenberg-Marquardt algorithm is performed in the null space of active constraints. Comparisons with optimization-based planners (CHOMP, TrajOpt, GPMP2) and sampling-based planners (RRT-Connect, RRT*, PRM) show the improved solution quality and feasibility, especially in constrained single- and multi-arm scenarios. The experimental evaluation of FACTO on Franka robots verifies the feasibility of deployment.

Generating collision-free and smooth motions remains a central challenge in robotic manipulation, particularly in cluttered environments and narrow passages where feasible regions are highly constrained and fragmented. We propose a trajectory optimization framework that performs geometry-aware updates directly in function space using natural functional gradients. The method optimizes a Gaussian-smoothed surrogate objective that regularizes the optimization landscape through smooth trajectory perturbations while preserving trajectory-level structure. Because the updates are defined intrinsically in function space, trajectory regularity can be controlled independently of a particular time discretization. We derive a practical Monte-Carlo estimator of the natural functional gradient that requires only black-box trajectory evaluations, making the method applicable when analytic gradients are unavailable or unreliable due to collision checking and contact-rich simulation. Experiments on constrained robotic manipulation tasks demonstrate that the proposed method improves trajectory feasibility and produces smoother motions than representative planning and trajectory optimization baselines in environments with narrow geometric clearances. Additional results, videos, and implementation details are available at the project page: https://kisangpark.github.io/natural-functional-gradient/

This paper proposes a task-oriented model predictive control (ToMPC) framework for safe and efficient robotic manipulation in open workspaces. The framework unifies collision-free motion and robot-environment interaction to address diverse scenarios. Additionally, it introduces task-oriented obstacle avoidance that leverages kinematic redundancy to enhance manipulation efficiency in obstructed environments. This complex optimization problem is solved by the alternating direction method of multipliers (ADMM), which decomposes the problem into two subproblems tackled by differential dynamic programming (DDP) and quadratic programming (QP), respectively. The effectiveness of this approach is validated in simulation and hardware experiments on a Franka Panda robotic manipulator. Results demonstrate that the framework can plan motion and/or force trajectories in real time, maximize the manipulation range while avoiding obstacles, and strictly adhere to safety-related hard constraints.