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An online method for obtaining smooth, jerk-bounded trajectories has been developed and implemented. Jerk limitation is important in industrial robot applications, since it results in improved path tracking and reduced wear on the robot. The method described herein uses a concatenation of fifth-order polynomials to provide a smooth trajectory between two way points. The trajectory approximates a linear segment with parabolic blends trajectory. A sine wave template is used to calculate the end conditions (control points) for ramps from zero acceleration to nonzero acceleration. Joining these control points with quintic polynomials results in a controlled quintic trajectory that does not oscillate, and is near time optimal for the jerk and acceleration limits specified. The method requires only the computation of the quintic control points, up to a maximum of eight points per trajectory way point. This provides hard bounds for online motion algorithm computation time. A method for blending these straight-line trajectories over a series of way points is also discussed. Simulations and experimental results on an industrial robot are presented.
Macfarlane et al. (2003) studied this question.
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