Redundant Robotic Manipulators I: Regularizing by Mechanical Impedance

Abstract

Redundancy is one of the main sources of skilled manipulation. We may distinguish between two types of redundancy: structural and task—dependent. The former type is a consequence of fixed constraints such as the presence of multiple actuators acting on a single joint. In contrast, kinematic redundancy may arise from specific task dependent requirements, as it is the case when we turn a steering wheel or we push a car with both hands. Both types of redundancy result in so called ill—posed problems, problems for which solutions either are not unique or do not exist due to an excess of constraints. Similar problems are also common in the study of artificial and natural vision [Poggio and Torre 1984].

Structural and task—dependent redundancy in complex anthropomorphic robots determine classes of ill—posed problems, i.e. problems for which it is difficult to identify unique solutions. We propose that the basic regularization mechanism is provided by the mechanical impedance of special actuators that, like the human muscles, are able to store elastic potential energy.

In particular, two kinds of distributed representations are proposed: (i) A Kinematic Net (K—net), that expresses the kinematic transformations and the causal relations implied by elasticity; (ii) A Topological Graph, that is based on a kinematic Robot Model, augmented and oriented according to the task and the connection to ground.

Two particularly significant results are: (i) the uniform treatment of closed as well as open kinematic chains, and (ii) the development of a new method for the automatic generation of kinematic equations with arbitrary topology.