Optimization of force distribution in redundantly actuated robotic systems.

摘要

This thesis presents an analysis of redundantly-actuated robotic systems with emphasis on systems which have a time-varying kinematic structure such as mechanical hands, walking machines and multiple manipulators grasping a common object.;The kinematic and dynamic equations governing the motion of these systems are then studied and compared to those of more conventional robotic systems. Although the inverse dynamics equations can be formulated in a number of ways, they always constitute an underdetermined system of linear equations. This allows their treatment as equality constraints in an optimization problem. In order to account for the limitations of passive contacts and actuator capabilities, inequality constraints are also considered.;The formulation of the optimization problem is then studied with emphasis on problems which are solvable in real-time and which produce time-continuous solutions. Quadratic programming is found to be a good choice of problem formulation. A quadratic-programming algorithm which efficiently includes both equality and inequality constraints is presented. A number of linear and quadratic objective functions which could be optimized are reviewed and the limitations of linear programming are made apparent through the use of numerical examples. Quadratic objective functions which minimize internal force, power consumption and solution discontinuities are examined. Finally, other applications of redundant actuation are briefly touched upon--the full dynamic balancing of linkages and the reduction of impact shocks in robotic systems.;Firstly, graph theory is used to characterize the kinematic structure of these systems and show that they can be decomposed into two subsystems, each with different properties. The contacts which occur between the constituent bodies in the system are then analyzed in order to determine the system's mobility (or number of degrees of freedom). It is found that this mobility varies during the task and that, at any given time, there will be more actuators active than are necessary.