A unified framework for dynamics and control of tree-type systems using exponential coordinates

摘要

This paper proposes a rapid and convenient method to model and control tree-type architecture systems using exponential coordinates. Exponential coordinates have elegant rules on products and derivatives, which allows for a simple definition of joint movements; and are highly effective for modeling complex architectures. The grasping and manipulation of an object by robot manipulators is considered in order to illustrate our modeling and control process. Using the chain matrix representing the system architecture, we derive a unified framework for the manipulator and object dynamics in a closed form fashion. The key benefit of this methodology is its simplicity and flexibility. Using this newly derived form of dynamics, we can conveniently change the system configurations (add/delete joints and links, change direction of joint movements, etc.) from one design to another; this will more accurately satisfy the manipulation requirements and simplify the optimization process for future system and control designs. Simulators can be conveniently constructed by following the formulas derived in the paper. Numerical examples of an arm-hand system are conducted to illustrate the usage of the proposed formulas in modeling, control, and optimization process. (C) 2019 Elsevier Ltd. All rights reserved.