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

The paper proposes a trajectory-optimization framework for redundant robotic multi-axis additive manufacturing, aimed at a hard problem: keeping long toolpaths collision-free while still hitting exact deposition positions. The authors combine a relative Jacobian formulation with a differentiable signed-distance-field collision model, so the optimizer can see both robot kinematics and the geometry changes caused by fabrication.

The key practical move is treating nozzle position as a hard waypoint-wise equality constraint, enforced by iterative projection onto the self-motion manifold. That lets the gradient stay in the tangent space of valid robot motion instead of drifting into infeasible poses. In experiments on an 8-DOF MAAM platform, the system held mean nozzle-position error below 10 μm, eliminated sampled collision and orientation violations, and reduced maximum joint jerk by up to 77.6%.

Compared with an SQP-based baseline, the method was up to 10.2x faster and converged more reliably. The paper also includes physical fabrication tests showing smoother trajectories and fewer visible deposition artifacts on complex geometries. Submission date was 29 Jun 2026, and the work sits at the intersection of robotics, computational geometry, and graphics.

For game developers, this is not directly a runtime-tech story, but it is relevant to anyone thinking about robotic fabrication, procedural manufacturing, or simulation-driven optimization. The broader takeaway is that differentiable collision models plus constrained projection can make long-horizon motion planning much...