Algebraic solution to minimum-time velocity planning

• Published in: International journal of control, automation, and systems Vol. 11; no. 4; pp. 805 - 814
• Main Authors: Lini, Gabriele, Piazzi, Aurelio, Consolini, Luca
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2013; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Algebra; Algorithms; Amplitudes; Analysis; Automation; Boundary conditions; Control; Control systems; Control Theory; Engineering; Maximum principle; Mechatronics; Navigation; Navigation systems; Optimization algorithms; Quartic equations; Real time; Robotics; Robots; Studies; Velocity; 제어계측공학; iterative steering; minimum-time control; Autonomous robotic navigation; feedforward control; Pontryagin’s Maximum Principle; velocity planning
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-011-0065-y

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.