S-Curve Trajectory Planning for Industrial Robots Based on Curvature Radius

Abstract

Motion planning in robotic systems, particularly in industrial contexts, must balance execution speed, precision, and safety. Excessive accelerations, especially centripetal ones in high, curvature regions, can cause vibrations, reduce tracking accuracy, and increase mechanical wear. This paper presents an off-line motion planning method that integrates curvature-based velocity modulation with jerk- and acceleration-limited S-curve profiles. The approach autonomously adjusts the speed along a predefined path according to local curvature by planning the motion at piecewise constant velocity and ensuring compliance with dynamic constraints on jerk, acceleration, and velocity. A non-linear filter tracks the velocity reference and smooths transitions while maintaining fluid motion, automatically adjusting velocity based on path curvature, ensuring smooth S-curve trajectories without requiring manual intervention. By jointly addressing geometric feasibility and dynamic smoothness, the proposed method reduces execution time while minimizing vibrations in applications involving abrupt curvature variations, as confirmed by its application to planar and spatial trajectories with varying curvature complexity. The method applies to smooth parametric trajectories and is not intended for paths with tangent discontinuities. The simulation results confirm full compliance with the imposed acceleration and jerk limits; nevertheless, future work will include experimental validation on realistic process trajectories and a quantitative performance assessment.