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_min ≤ x˙(t) ≤ V_max, A_min ≤ x¨(t) ≤ A_max and |x¨˙| ≤ 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.