Algebraic solution to minimum-time velocity planning

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...

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Bibliographic Details
Published in:International journal of control, automation, and systems 2013, Automation, and Systems, 11(4), , pp.805-814
Main Authors: Lini, Gabriele, Piazzi, Aurelio, Consolini, Luca
Format: Article
Language:English
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
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Summary: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.
ISSN:1598-6446
2005-4092
DOI:10.1007/s12555-011-0065-y