Low-harmonic rational Bezier and spline curves for joint trajectory synthesis with actuator dynamics response limitations

This paper deals with joint trajectory synthesis for robot manipulators with consideration of the dynamic response limitations of their actuators. During a robot motion, the higher harmonics present in the actuating torques (forces) may excite the natural modes of oscillation of the robot manipulator. The purpose of this paper is to develop a method for synthesizing joint trajectories that are least susceptible to vibrational excitation. We show that a low-harmonic trajectory pattern corresponds to a special class of rational Bezier curves with a set of specially selected weights. We study C³ conditions for piecing two low-harmonic rational Bezier curve-segments and develop a geometric algorithm for constructing low-harmonic rational spline curves. Finally, we discuss how these low-harmonic curves may be used to design joint trajectories that are least susceptible to vibrational excitation.