Trajectory Optimization for Collision-Aware Redundant Robotic Multi-Axis Additive Manufacturing by Constrained Gradient Projection

2026-06-29

AI Summary

This work addresses the challenge of trajectory optimization for long-range paths in redundant robotic multi-axis additive manufacturing under stringent deposition position constraints and time-varying collision constraints. The authors propose a collision-aware trajectory optimization framework that models the kinematic relationship between the nozzle and workpiece using relative Jacobians, captures dynamic geometric evolution through differentiable signed distance fields (SDFs), and enforces hard deposition position constraints via iterative projection onto the self-motion manifold. Optimization efficiency is enhanced by restricting gradient updates to the tangent space. Experimental results on an 8-degree-of-freedom platform demonstrate sub-10-micron average nozzle positioning error, a 77.6% reduction in peak joint jerk, complete avoidance of collisions and posture violations, up to a 10.2× speedup over an SQP baseline, and successful fabrication of complex unsupported structures.

Abstract

Redundant robotic multi-axis additive manufacturing (MAAM) enables support-free and conformal fabrication, but trajectory optimization for long-horizon paths remains challenging under strict deposition-position constraints and time-varying collision constraints. This work proposes a computational framework for collision-aware trajectory optimization in redundant robotic MAAM. We first formulate nozzle-workpiece relative kinematics using a relative Jacobian, and develop a differentiable SDF-based collision model that captures fabrication-induced geometry evolution and provides optimization gradients. The deposition position is then enforced as a hard waypoint-wise equality constraint through iterative projection onto the self-motion manifold, with the loss gradient restricted to the corresponding tangent space. Experiments on an 8-DOF robotic MAAM platform with diverse long-horizon support-free and conformal toolpaths show that our method maintains a mean nozzle-position error below 10μm, reduces maximum joint jerk by up to $77.6\%$, and eliminates all sampled collision and orientation violations. Compared with the SQP-based baseline, it achieves up to a 10.2x speedup and improved convergence. Physical fabrication experiments further verify that the resulting smooth, collision-free trajectories enable successful printing of complex geometries with fewer visible deposition artifacts.

Problem

• trajectory optimization
• collision avoidance
• redundant robotic MAAM
• deposition-position constraints
• time-varying collision constraints

Innovation

• trajectory optimization
• redundant robotic MAAM
• collision-aware planning
• differentiable SDF
• self-motion manifold