Hybrid Dynamics and Other Topics

Abstract

This chapter covers the following topics: hybrid dynamics, floating bases, gears and dynamic equivalence. Hybrid dynamics is a generalization of forward and inverse dynamics in which the forces are known at some joints, the accelerations at the rest, and the task is to calculate the unknown forces and accelerations. In effect, one is performing forward dynamics at some joints and inverse dynamics at the rest. A floating-base system is one in which the base is a moving body. Such systems can be modelled as fixed-base systems by installing a 6-DoF joint between the fixed base and the body representing the floating base. However, floating-base systems are an important class of rigid-body systems, and merit special treatment. Sections 9.1 to 9.5 present several algorithms for hybrid dynamics and floating bases. Gears impose constraints between joint variables. They therefore resemble kinematic loops, and Section 9.6 shows how gear constraints can be incorporated into a rigid-body system using a technique that was developed in Chapter 8 for kinematic loops. Two different rigid-body systems are dynamically equivalent if they have the same equation of motion. Section 9.7 explores this concept, and presents a method for modifying the inertia parameters of a rigid-body system without altering its equation of motion.