Should We Forget the Jerk in Trajectory Generation?

This article explores whether jerk, the derivative of acceleration, should be limited in trajectory planning for position-controlled mechanical systems or in the controller. The excess jerk excites structural resonances and increases actuator wear, motivating the use of a limited jerk. However, we question the necessity of incorporating the jerk directly in trajectory planning by comparing third-order jerk-limited trajectories with second-order trajectories with reduced controller bandwidth that regulate torque gradients. We demonstrate by a typical practical application that reducing controller bandwidth can achieve comparable or superior jerk reduction without extending overall motion time for point-to-point trajectories. As a result, second-order parabolic trajectory profiles simplify on-line implementation. This investigation relies on a detailed sensitivity analysis of a one-dimensional model, incorporating crucial elements such as signal and sensor quantisation, sampling, and modes of structural resonances. The study shows that smooth trajectories reduce resonant vibrations and wear, but the jerk limitation may be addressed more effectively within the controller rather than within the trajectory generator. We conclude that although the limitation of the jerk in the trajectories is valuable, feedback controllers can reduce the jerk more effectively by bandwidth reduction, allowing simpler point-to-point trajectory designs without compromising performance.