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We present Ruckig, an algorithm for Online Trajectory Generation (OTG)respecting third-order constraints and complete kinematic target states. Givenany initial state of a system with multiple Degrees of Freedom (DoFs), Ruckigcalculates a time-optimal trajectory to an arbitrary target state defined byits position, velocity, and acceleration limited by velocity, acceleration, andjerk constraints. The proposed algorithm and implementation allows threecontributions: (1) To the best of our knowledge, we derive the firsttime-optimal OTG algorithm for arbitrary, multi-dimensional target states, inparticular including non-zero target acceleration. (2) This is the firstopen-source prototype of time-optimal OTG with limited jerk and complete timesynchronization for multiple DoFs. (3) Ruckig allows for directional velocityand acceleration limits, enabling robots to better use their dynamicalresources. We evaluate the robustness and real-time capability of the proposedalgorithm on a test suite with over 1,000,000,000 random trajectories as wellas in real-world applications.

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