Third order trajectory generator satisfying velocity, acceleration and jerk constraints

A third order continuous-time trajectory generator useful in motion control systems is presented. The proposed nonlinear system receives as input a standard reference signal r(t) (step, ramp, etc.) and provides as output a smooth signal x(t) satisfying the following constraints on velocity, acceleration and jerk: V/sub min/ /spl les/ x/spl dot/(t) /spl les/ V/sub max/, A/sub min/ /spl les/ x/spl uml/(t) /spl les/ A/sub max/ and |x/spl uml//spl dot/| /spl les/ U. The generated trajectory tracks the reference signal in minimum time compatible with the constraints on the time derivatives. The performance of the presented trajectory generator is tested in simulation.