Robust control of dynamically interacting systems

Dynamic interaction with the environment is fundamental to the process of manipulation. This paper describes an approach to the design of ‘interaction controllers’ and contrasts this with an approach to servo design. The need for ‘coupled stability’ and ‘interactive behaviour’ specifications is motivated. A necessary and sufficient condition to ensure the stability of a linear manipulator coupled at a single interaction port to a linear, passive environment is found. It is shown that this condition may be extended to a broad class of active environments, and a simple test for coupled stability, based on the root locus, is presented. Two interaction controller designs for a linear manipulator are presented. Interactive behaviour is analysed in the frequency domain by comparison with the behaviour of a target model. A simple controller shows strong stability properties, but poor behaviour; a more sophisticated design shows that it is possible to achieve desirable behaviour while retaining stability guarantees.