Robot dynamics algorithms

Abstract

In this dissertation I introduce a new notation for representing rigid-body dynamics, and use it to describe a number of methods for calculating robot dynamics efficiently. The notation (called spatial notation) is based on the use of 6- dimensional vectors (called spatial vectors) which combine the linear and angular aspects of rigid-body dynamics. Spatial vectors are similar to quantities called screws and motors. The use of spatial notation allows a more concise treatment of problems in rigid-body dynamics than is possible by the conventional vector approach by reducing the number of quantities required to describe a system and the number and size of equations relating those quantities. I consider both forward and inverse robot dynamics, though I am concerned mainly with forward dynamics. Three basic algorithms are described: the recursive Newton-Euler method for inverse dynamics, and the composite-rigid-body and articulated-body methods for forward dynamics. The articulated-body method is new, and is based on the use of quantities called articulated-body inertias which relate the force applied to a member of a linkage to the acceleration induced in that member, taking into account the effect of the rest of the link¬ age. Once the basic algorithms have been introduced, I consider some aspects of their implementation on a computer, then I describe vari¬ ous extensions of the basic algorithms to cater for generalisations of the robot's structure, including multiple-degree-of-freedom joints and branched kinematic chains. Finally, I consider the problem of simulating contact and impact between the robot and its environment.