Optimal Path Planning for Nonholonomic Robotic Systems via Parametric Optimisation

  • James Biggs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6856)


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. 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.


Cost Function Optimal Control Problem Path Planning Autonomous Underwater Vehicle Nonholonomic System 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • James Biggs
    • 1
  1. 1.Advanced Space Concepts Laboratory, Department of Mechanical EngineeringUniversity of StrathclydeGlasgowUK

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