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We present a novel trajectory computation algorithm to smooth jerky collision-free paths computed by samplebased motion planners. Our approach uses cubic B-splines to generate G2 or curvature continuous trajectories. The algorithm performs local spline refinement to compute smooth, collision-free paths in narrow passages and satisfy velocity and acceleration constraints. We also present a fast and reliable algorithm for collision checking between robot and the environment along the B-spline trajectories. We highlight the performance of our algorithm on complex benchmarks, including path computation for rigid and articulated models in tight spaces and cluttered environments.