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Optimal path planning for nonholonomic robotics systems via parametric optimisation

Biggs, James (2011) Optimal path planning for nonholonomic robotics systems via parametric optimisation. In: Lecture Notes in Computer Science. Springer. ISBN 978-3-642-23231-2

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Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping.

Item type: Book Section
ID code: 32125
Keywords: algorithmic learning, autonomous robots, mobile robot navigation, personal robots, robot agents, robot emotions, robot routing, artificial intelligence, HCI, image processing, Mechanical engineering and machinery, Motor vehicles. Aeronautics. Astronautics, Mechanical Engineering, Aerospace Engineering, Control and Systems Engineering, Computational Mechanics
Subjects: Technology > Mechanical engineering and machinery
Technology > Motor vehicles. Aeronautics. Astronautics
Department: Faculty of Engineering > Mechanical and Aerospace Engineering
Technology and Innovation Centre > Advanced Engineering and Manufacturing
Depositing user: Pure Administrator
Date Deposited: 13 Jul 2011 09:45
Last modified: 21 Jul 2015 20:26
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