We present Ruckig, an algorithm for Online Trajectory Generation (OTG) respecting third-order constraints and complete kinematic target states. Given any initial state of a system with multiple Degrees of Freedom (DoFs), Ruckig calculates a time-optimal trajectory to an arbitrary target state defined by its position, velocity, and acceleration limited by velocity, acceleration, and jerk constraints. The proposed algorithm and implementation allows three contributions: (1) To the best of our knowledge, we derive the first OTG algorithm with non-zero target acceleration, resulting in a complete defined target state . (2) This is the first open-source prototype of time-optimal OTG with limited jerk  . (3) Ruckig allows for directional velocity and acceleration limits, enabling robots to better use their dynamical resources. We evaluate the robustness and real-time capability of the proposed algorithm on a test suite with over 1,000,000,000 random trajectories as well as in real-world applications.
We present Ruckig, an algorithm for Online Trajectory Generation (OTG) respecting third-order constraints and complete kinematic target states. Given any initial state of a system with multiple Degrees of Freedom (DoFs), Ruckig calculates a time-optimal trajectory to an arbitrary target state defined by its position, velocity, and acceleration limited by velocity, acceleration, and jerk constraints. The proposed algorithm and implementation allows three contributions: (1) To the best of our knowledge, we derive the first time-optimal OTG algorithm for arbitrary, multi-dimensional target states, in particular including non-zero target acceleration . (2) This is the first open-source prototype of time-optimal OTG with limited jerk and complete time synchronization for multiple DoFs . (3) Ruckig allows for directional velocity and acceleration limits, enabling robots to better use their dynamical resources. We evaluate the robustness and real-time capability of the proposed algorithm on a test suite with over 1,000,000,000 random trajectories as well as in real-world applications.
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OTG algorithm with
time-optimal OTG algorithm for arbitrary, multi-dimensional target states, in particular including
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acceleration, resulting in a complete defined target state
acceleration
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and complete time synchronization for multiple DoFs