Planning Jerk-Optimized Trajectory with Discrete-Time Constraints for Redundant Robots

TL;DR

The paper tackles planning jerk-minimized trajectories for redundant robots under thousands of discrete time constraints in robotic fabrication. It combines a graph-based, resolution-complete initialization with adaptive local jerk filtering and a learning-based collision estimator to handle high-dimensional configuration spaces efficiently. Key contributions include a greedy local filtering algorithm with window-adaptation and locking, a contact-space–focused sampling strategy for training an algebraic collision surrogate via SVM-RBF, and substantial empirical gains in jerk reduction and planning speed demonstrated on 6- and 8-DOF robotic fabrication platforms. The work enables smoother, higher-quality robotic fabrication while maintaining tractable planning times, with limitations mainly in global optimality and dynamic environments—pointing to future integration with global planners and robustness enhancements.

Abstract

We present a method for effectively planning the motion trajectory of robots in manufacturing tasks, the tool-paths of which are usually complex and have a large number of discrete-time constraints as waypoints. Kinematic redundancy also exists in these robotic systems. The jerk of motion is optimized in our trajectory planning method at the meanwhile of fabrication process to improve the quality of fabrication.

Figures (14)

• Figure 1: An example tool-path for robot-assisted 3D printing system dai18, rotation around the red axis can be freely changed because of kinematic redundancy.
• Figure 2: An illustration for the graph used in our approach to find an initial trajectory. Nodes in the same column (called ladder) represent the different feasible solutions in the joint space for realizing the same way point. Edges are added between nodes in neighboring ladders. The shortest path on the graph is highlighted by the blue dashed lines.
• Figure 3: The change of the maximum jerk at each joint during the iterations of our method. The maximal jerk has been reduced by $83.6\%-95.8\%$ on all the six joints. The dash line shows the allowed maximal jerk as $j_{\max}=1.0$ in this example.
• Figure 4: The total sum of squared jerks, $\mathbb{J}$ in Eq.(\ref{['eqGlobalOptm']}), on the trajectory is effectively reduced during the iterations of our method. The value has been reduced by $99.4\%$ on the final result.
• Figure 5: A 3-DOF planar robotic arm for tracing a 2D path (green) with obstacles (red). The example is used to study the effectiveness of our sampling strategy for learning the collision-indication function. As shown in the right, the C-space of contact $\mathcal{Q}_{cont}$ is displayed by blue color for the collision-free region (i.e., $\mathcal{Q}_{cont} \cap \mathcal{Q}_{free}$) and gray color for the collided region (i.e., $\mathcal{Q}_{cont} \cap \overline{\mathcal{Q}_{free}}$). Note that, the white regions in the configuration space are not reachable by the robotic arm.