Abstract
Abstract. This paper addresses the motion planning problem in non-holonomic robotic systems. The system's kinematics and dynamics are represented as a control affine system with outputs. The problem is defined in terms of the end-point map of this system, using the endogenous configuration space approach. Special attention is paid to the multiple-task motion planning problem, i.e. a problem that beyond the proper motion planning task includes a number of additional tasks. For multiple-task motion planning two strategies have been proposed, called the egalitarian approach and the prioritarian approach. Also, two computational strategies have been launched of solving the motion planning problem: the parametric and the non-parametric. The motion planning and computational strategies have been applied to a motion planning problem of the trident snake robot. Performance of the motion planning algorithms is illustrated with computer simulations.
Highlights
The motion planning problem of a robotic system consists in determining an action in the configuration space that would drive the system along a desired trajectory or to a desired location in the task space
Founded on the end-point map of a control system, the endogenous configuration space approach extends in a natural way to robotic systems with dynamics (Zadarnowska and Tchon, 2007; Ratajczak et al, 2010)
Since the dynamics of a non-holonomic robotic system can be represented as an affine control system with outputs, this system will define our universe of discourse
Summary
The motion planning problem of a robotic system consists in determining an action in the configuration space that would drive the system along a desired trajectory or to a desired location in the task space. Founded on the end-point map of a control system, the endogenous configuration space approach extends in a natural way to robotic systems with dynamics (Zadarnowska and Tchon, 2007; Ratajczak et al, 2010). This analysis has been extended to the case of active wheels in Paszuk et al (2012) and complemented by a study of trident snake dynamics (Pietrowska, 2012) In both these cases the motion single-task planning algorithms have been derived from the endogenous configuration space approach. Two computational strategies have been proposed in order to solve the motion planning problem: the parametric and the non-parametric, depending on whether the computation of the control function utilizes a specific base in the endogenous configuration space or is base-independent. In order to not distract the reader’s attention from the main thread of the paper, a derivation of the subtask Jacobian and its inverse as well as the dynamics model of the trident snake are placed in the Appendix
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