Robot Joint Motion Control via Parabola Trajectory

The patent applies curvature by replacing linear connecting trajectories with circular arc trajectories. The circular arc trajectory is defined by calculating key points (start point, end point, and midpoint) and using them to generate a smooth curved path that eliminates the stiffness and overshoot problems of linear control while maintaining implementation simplicity through standardized circular arc calculations.

The patent applies preliminary action by pre-calculating the circular arc trajectory key points (start point, end point, and midpoint) before execution. The midpoint is specifically calculated in advance to define the curvature of the trajectory, allowing the control system to smoothly transition between joint positions without sudden disconnects that cause overshoot and shake.

The patent replaces linear control with circular arc trajectory control, where the trajectory is defined by three key points (start, end, and midpoint). This curved path approach significantly improves joint motion smoothness and eliminates the mechanized, stiff appearance of linear control while maintaining reasonable computational cost through efficient circular arc calculations.