ABSTRACT
SUMMARY This chapter gives a full derivation of the dynamics and control of multiple rigid bodies in a 3-D space. Almost all existing control literature concentrates on point mass systems. Although there is wide coverage of multiple degrees of freedom in the literature, they are not representative of realistic situations. Modeling of the dynamics of rigid bodies presents difficulties as far as the modeling of spring and damper elements are concerned. The same difficulties are also related to the actuator elements. A further complication is due to the fact that actuator dynamics are influenced by the kinematics of their assembly points as well as feedback from sensors. What a sensor measures in a rigid body environment is the point motion on a rigid body, which is made of up to six degrees of motion relating to the rigid body, or if it is measuring motion between two moving bodies, then 12 degrees are involved. What is measured sometimes is in one direction (a typical accelerometer); therefore, there is no possibility of knowing state variables that generate such motion uniquely. Not having a unique relationship to state variables complicates the feedback control strategy. All these considerations make rigid body control a challenging task. The present chapter deals with these issues and offers a complete mathematical treatment to the problem.
