Operational Space Control: A Theoretical and Empirical Comparison

Dexterous manipulation with a highly redundant movement system is one of the hallmarks of human motor skills. From numerous behavioral studies, there is strong evidence that humans employ compliant task space control, i.e. they focus control only on task variables while keeping redundant degrees-of-freedom as compliant as possible. This strategy is robust towards unknown disturbances and simultaneously safe for the operator and the environment. The theory of operational space control in robotics aims to achieve similar performance properties. However, despite various compelling theoretical lines of research, advanced operational space control is hardly found in actual robotics implementations, in particular new kinds of robots like humanoids and service robots, which would strongly profit from compliant dexterous manipulation. To analyze the pros and cons of different approaches to operational space control, this paper focuses on a theoretical and empirical evaluation of different methods that have been suggested in the literature, but also some new variants of operational space controllers. We address formulations at the velocity, acceleration, and force levels. First, we formulate all controllers in a common notational framework, including quaternion-based orientation control, and discuss some of their theoretical properties. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm with several benchmark tasks. As an aside, we also introduce a novel parameter estimation algorithm for rigid body dynamics, which ensures physical consistency, as this issue was crucial for our successful robot implementations. Our extensive empirical results demonstrate that one of the simplified acceleration-based approaches can be advantageous in terms of task performance, ease of parameter tuning, and general robustness and compliance in the face of inevitable modeling errors.