Collision-free and smooth motion planning of dual-arm Cartesian robot based on B-spline representation

This paper discusses a new approach to motion planning of dual-arm gantry kinematic that solves the self-collision problem while ensuring G2-continuity and low curvatures. Starting from collision-free start and target points, the proposed method defines the geometric path of the end-effectors with classical five-segment planar trajectories, described by fifth-degree B-splines. The rototraslation of the loaded parts is evaluated in frames to define sampled overlapping curves, used to compute splines that act as deviation curves being added on the previously defined geometric paths in order to prevent collisions. Here, a quadratic programming minimization is employed to reduce the curvature of these spline and preserve the kinematics properties of the initial path. The kinematic constraints of the axes are ensured by iso-parametric trajectory planning, which results in an optimized motion profile to reduce the task execution time. Finally, the proposed approach is applied to a sorting system for laser machine (LST) having a dual-arm 7-d.o.f. gantry kinematic. The results of a case study of a typical sorting operation are presented and discussed to illustrate and clarify the method. The approach presented in this work can be applied to other robotic systems with similar kinematic structures, providing a useful tool for motion planning in pick-and-place applications.