Jerk-limited Real-time Trajectory Generation with Arbitrary Target States

We present Ruckig, an algorithm for Online Trajectory Generation (OTG)\nrespecting third-order constraints and complete kinematic target states. Given\nany initial state of a system with multiple Degrees of Freedom (DoFs), Ruckig\ncalculates a time-optimal trajectory to an arbitrary target state defined by\nits position, velocity, and acceleration limited by velocity, acceleration, and\njerk constraints. The proposed algorithm and implementation allows three\ncontributions: (1) To the best of our knowledge, we derive the first\ntime-optimal OTG algorithm for arbitrary, multi-dimensional target states, in\nparticular including non-zero target acceleration. (2) This is the first\nopen-source prototype of time-optimal OTG with limited jerk and complete time\nsynchronization for multiple DoFs. (3) Ruckig allows for directional velocity\nand acceleration limits, enabling robots to better use their dynamical\nresources. We evaluate the robustness and real-time capability of the proposed\nalgorithm on a test suite with over 1,000,000,000 random trajectories as well\nas in real-world applications.\n