Accession Number : ADA261746


Title :   A Surface Integral Algorithm for the Motion Planning of Nonholonomic Mechanical Systems


Descriptive Note : Master's thesis


Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA


Personal Author(s) : Anderson, David P


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a261746.pdf


Report Date : Dec 1992


Pagination or Media Count : 66


Abstract : The number of coordinates needed to completely describe the configuration of a holonomic mechanical system is equal to the number of degrees of freedom possessed by that system. In contrast, nonholonomic systems always require more coordinates for their description than there are degrees of freedom due to the nonintegrable nature of the governing velocity constraints. The task of nonholonomic motion planning applied to a given system is to develop trajectories of the independent coordinate variables such that the entire system is driven to some desired point in its configuration space. An algorithm for constructing these trajectories is presented. In this algorithm, the independent variables are first converged to their desired values. The dependent variables are subsequently converged using closed trajectories of the independent variables. The requisite closed trajectories are planned using Stoke's Theorem, which converts the problem of finding a closed path in the space of the independent variables to that of finding a surface area in that same space such that the dependent variables converge to their desired values as the independent variables traverse along the boundary of the surface area. The use of Stoke's Theorem simplifies the motion planning process and also answers important questions pertaining to the system. The salient features of the algorithm are apparent in the two examples discussed: a planar space robot and a disk rolling without slipping on a flat surface.


Descriptors :   *ALGORITHMS , *ROBOTS , *COORDINATES , *MOTION , *MECHANICAL ENGINEERING , VELOCITY , VARIABLES , BOUNDARIES , TRAJECTORIES , THEOREMS , ASTRONAUTICS , DISKS , CONFIGURATIONS , PLANNING , DEGREES OF FREEDOM , THESES , PATHS , ROBOTICS


Subject Categories : Numerical Mathematics
      Cybernetics
      Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE