Monday, November 22, 1999

(Dr. Steve Dickerson, advisor)

"Jerk Limited Trajectory Generation for Motion Control"

__Abstract__

A jerk limited reference trajectory refers to a position profile whose derivative profiles satisfy maximum constraints. The velocity, acceleration, and jerk profiles are each bounded by maximums. As we shall see, constraints on the value of jerk implies certain degrees of smoothness in acceleration, velocity, and position profiles. Jerk limited trajectories can also be said to encompass the set of trajectories that reflect a limit in the rate of change of force applicable to a mass by a motor. These trajectories accommodate for the physical limitations of the motor and, therefore, do not command the motor to do anything it cannot accomplish. Trajectories that fall under this class can be tracked well by a machine. Precise motion control of an electric motor driven machine requires that the motor not be commanded to deliver more speed, more torque, nor rate of change of torque than is physically realizable. As alluded to earlier, the trajectories developed here also stipulate that the acceleration profile is continuous to minimize trajectory-related induced vibration in the mass. Instantaneous changes in the applied force to a mass will tend to excite vibrations. By constraining the acceleration profile to be continuous, however, will lower the reference trajectory as a source of induced vibration in the machine/mass system.

The task is to develop methods for generating jerk limited trajectories that maximize the potential of the test machine while conforming to the physical limitations of the hardware. Three approaches will be considered.

- Given the endpoints, the motion trajectories are generated based on the dynamic constraints.
- Given points along the trajectory at a rate lower than the servo rate, points on the path are calculated at the desired rate through interpolation.
- Given a trajectory, at the desired servo rate, which violates the dynamic constraints, an acceptable trajectory is acquired by passing the deviant trajectory through a FIR filter.