An Integrated Approach to Robotic Joint Interpolation: Kinematic Modeling and Constraints for Smooth Trajectories

This paper introduces a direct trajectory planning approach for manipulator robots, seamlessly transitioning from the task space to the robot joint space, while adhering to kinematic (joint position and velocity boundaries) and dynamic (torque limits) constraints. The proposed method employs state-space modeling utilizing joint positions and their derivatives up to order n-1 as state variables, and the nth derivative of joint positions as the control signal to guarantee continuity and differentiability during interpolation. Furthermore, the output of the statespace model created are the forward and differential kinematics of the robot, enabling interpolation with consideration for posture (position and orientation) and velocity (linear and angular) in the task space. Thereby, the optimal control signal computation is derived via the minimization of the Square Error between the state-space’s output with the desired final output through quasi-Newton optimization. Then, the calculation of joint values over time is achieved via the nth integration of the previously computed control signal using the Cauchy formula for repeated integration. Finally, the proposed method is validated on the ABB-IRB-120 robot model, where it demonstrates a unified solution for task-space path planning under both kinematic and dynamic constraints.