Quaternion-Based Velocity Scheduling for Robotic Systems

Finding the time-optimal parameterization of a given path subject to kinodynamic constraints is a critical topic in many robotic applications. However, designing a real-time motion planning algorithm for specified trajectories subject to physical constraints is challenging due to the high nonlinearity in robotic systems. Additionally, moving along a given path may include three types of motion—pure translation, pure orientation, and composite motion—which will further complicate finding the best solution in these applications. To cope with this difficulty, this paper proposes a complete, real-time quaternion-based velocity scheduling algorithm (QBVSA) that takes physical constraints such as joint velocity, joint acceleration, and joint torque into account. The proposed QBVSA is designed to efficiently handle various types of motion subject to physical constraints in real-time. The completeness of the proposed QBVSA is proved mathematically. By exploiting the idea of the initial velocity limit, the search for switching points—which is essential to the conventional numerical integration method—is not required in the proposed approach. Simulations and experiments are performed to validate the proposed motion planning approach.