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

--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. Our method is based on a sampling strategy and consists of two major parts. After determining an initial path by graph-search, a greedy algorithm is adopted to optimize a path by locally applying adaptive filers in the regions with large jerks. The filtered result is obtained by numerical optimization. In order to achieve efficient computation, an adaptive sampling method is developed for learning a collision-indication function that is represented as a support-vector machine. Applications in robot-assisted 3D printing are given in this paper to demonstrate the functionality of our approach. Abstract --In robot-assisted manufacturing applications, robotic arms are employed to realize the motion of workpieces (or machining tools) specified as a sequence of waypoints with the positions of tool tip and the tool orientations constrained. The required degree-of-freedom (DOF) is often less than the robotic hardware system (e.g., a robotic arm has 6-DOF). Specifically, rotations of the workpiece around the axis of a tool can be arbitrary (see Figure 1 for an example). By using this redundancy - i.e., there are many possible poses of a robotic arm to realize a given waypoint, the trajectory of robots can be optimized to consider the performance of motion in velocity, acceleration and jerk in the joint space. In addition, when fabricating complex models each tool-path can have a large amount of waypoints. It is crucial for a motion planning algorithm to compute a smooth and collision-free trajectory of robot to improve fabrication quality. The time taken by the planning algorithm should not significantly lengthen the total manufacturing time; ideally it would remain hidden as computing motions for a layer can be done while the previous layer is printing. The method presented in this paper provides an efficient framework to tackle this problem. The framework has been well tested on our robot-assisted additive manufacturing system to demonstrate its effectiveness and can be generally applied to other robot-assisted manufacturing systems.