Minimum energy trajectory planning for robotic manipulators

TLDR: This dissertation develops a practical approach to the planning of minimum energy consumpt~on trajectories for robotic manipulators by searching for an optimum among a class of functions which can be described by a fixed number of parameters; namely spline functions.

Abstract: This dissertation develops a practical approach to the planning of minimum energy consumpt~on trajectories for robotic manipulators. That is, a trajectory is sought between ' given initial and final states such that the energy consumption is minimized. This functional optimization problem may be described using classical variational theory. However, the two-point-boundary-value problem which arises from this formulation is practically insoluble. Therefore, the problem is converted to a function optimization by searching for an optimum among a class of functions which can be described by a fixed number of parameters; namely spline functions. Conversion to a function optimization problem allows a large number of numerical function optimization methods to be attempted. Methods attempted in this work are Powell's method, interval methods, genetic algorithms, simulated annealing and dynamic programming. Each of these methods are found to be wanting in some respects. Powell's method is a local optimization procedure. As such, it tends to get trapped in local minima. Interval methods, while interesting in that they provide the promise of a global optimum, fail, since a suitable interval bounding function for the energy consumption is not available. Genetic algorithms, simulated annealing and dynamic programming alJ require excessive computational effort. To overcome these difficulties, the basic dynamic programming method is modified to perform a series of dynamic programminp, passes over a small reconfigurable grid covering only a portion of the solution space at any one pass, rather than attempt to perform a single dynamic programming operation over a large tightly spaced grid. Although this modification changes the dynamic programming approach from a global to a local