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Algebraic Solution to Minimum-Time Velocity Planning
Gabriele Lini,Aurelio Piazzi,Luca Consolini 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.4
The paper poses the problem of minimum-time velocity planning subject to a jerk amplitude constraint and to arbitrary velocity/acceleration boundary conditions. This problem which is relevant in the field of autonomous robotic navigation and also for inertial one-dimensional mechatronics systems is dealt with an algebraic approach based on Pontryagin’s Maximum Principle. The exposed complete solution shows how this time-optimal planning can be reduced to the problem of determining the positive real roots of a quartic equation. An algorithm that is suitable for real-time applications is then presented. The paper includes detailed examples also highlighting the special cases of this planning problem.