Optimal path planning for nonholonomic robotics systems via parametric optimisation

James Biggs

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.
LanguageEnglish
Title of host publicationLecture Notes in Computer Science
Subtitle of host publicationTowards Autonomous Robotic Systems
PublisherSpringer
Number of pages12
Volume6856
Edition1st
ISBN (Print)978-3-642-23231-2
Publication statusPublished - 17 Aug 2011
Event12th Conference Towards Autonomous Robotic Systems 2011 - Sheffield , United Kingdom
Duration: 31 Aug 20112 Sep 2011

Conference

Conference12th Conference Towards Autonomous Robotic Systems 2011
CountryUnited Kingdom
CitySheffield
Period31/08/112/09/11

Fingerprint

Motion planning
Robotics
Cost functions
Kinematics
Hamiltonians
Maximum principle
Angular velocity
Damping
Trajectories
Boundary conditions
Robots

Keywords

  • algorithmic learning
  • autonomous robots
  • mobile robot navigation
  • personal robots
  • robot agents
  • robot emotions
  • robot routing
  • artificial intelligence
  • HCI
  • image processing

Cite this

Biggs, J. (2011). Optimal path planning for nonholonomic robotics systems via parametric optimisation. In Lecture Notes in Computer Science: Towards Autonomous Robotic Systems (1st ed., Vol. 6856). Springer.
Biggs, James. / Optimal path planning for nonholonomic robotics systems via parametric optimisation. Lecture Notes in Computer Science: Towards Autonomous Robotic Systems. Vol. 6856 1st . ed. Springer, 2011.
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Biggs, J 2011, Optimal path planning for nonholonomic robotics systems via parametric optimisation. in Lecture Notes in Computer Science: Towards Autonomous Robotic Systems. 1st edn, vol. 6856, Springer, 12th Conference Towards Autonomous Robotic Systems 2011, Sheffield , United Kingdom, 31/08/11.

Optimal path planning for nonholonomic robotics systems via parametric optimisation. / Biggs, James.

Lecture Notes in Computer Science: Towards Autonomous Robotic Systems. Vol. 6856 1st . ed. Springer, 2011.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Biggs J. Optimal path planning for nonholonomic robotics systems via parametric optimisation. In Lecture Notes in Computer Science: Towards Autonomous Robotic Systems. 1st ed. Vol. 6856. Springer. 2011