Nonholonomic motion planning for a freefalling cat using spline approximation
Abstract
An optimal motion planning of a freefalling cat based on the spline approximation is investigated. Nonholonomicity arises in a freefalling cat subjected to nonintegrable velocity constraints or nonintegrable conservation laws. The equation of dynamics of a freefalling cat is obtained by using the model of two symmetric rigid bodies. The control of the system can be converted to the motion planning problem for a driftless system. A cost function is used to incorporate the final errors and control energy. The motion planning is to determine control inputs to minimize the cost function and is formulated as an infinite dimensional optimal control problem. By using the control parameterization, the infinite dimensional optimal control problem can be transformed to a finite dimensional one. The particle swarm optimization (PSO) algorithm with the cubic spline approximation is proposed to solve the finite dimension optimal control problem. The cubic spline approximation is introduced to realize the control parameterization. The resulting controls are smooth and the initial and terminal values of the control inputs are zeros, so they can be easily generated by experiment. Simulations are also performed for the nonholonomic motion planning of a freefalling cat. Simulated experimental results show that the proposed algorithm is more effective than the Newtoian algorithm.
 Publication:

Science China Physics, Mechanics, and Astronomy
 Pub Date:
 November 2012
 DOI:
 10.1007/s1143301248916
 Bibcode:
 2012SCPMA..55.2100G
 Keywords:

 falling cat;
 nonholonomic constraint;
 motion planning;
 spline approximation;
 particle swarm optimization