title: Quantifying control effort of biological and technical movements: an information-entropy-based approach.
abstract: In biomechanics and biorobotics, muscles are often associated with reduced movement control effort and simplified control compared to technical actuators. This is based on evidence that the nonlinear muscle properties positively influence movement control. It is, however, open how to quantify the simplicity aspect of control effort and compare it between systems. Physical measures, such as energy consumption, stability, or jerk, have already been applied to compare biological and technical systems. Here a physical measure of control effort based on information entropy is presented. The idea is that control is simpler if a specific movement is generated with less processed sensor information, depending on the control scheme and the physical properties of the systems being compared. By calculating the Shannon information entropy of all sensor signals required for control, an information cost function can be formulated allowing the comparison of models of biological and technical control systems. Exemplarily applied to (bio-)mechanical models of hopping, the method reveals that the required information for generating hopping with a muscle driven by a simple reflex control scheme is only I=32 bits versus I=660 bits with a DC motor and a proportional differential controller. This approach to quantifying control effort captures the simplicity of a control scheme and can be used to compare completely different actuators and control approaches.
authors.affiliation: Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Germany and Universität Stuttgart, Institut für Theoretische Physik 1, Pfaffenwaldring 57, D-70550 Stuttgart, Germany.
authors.forename: D F B
authors.initials: DF
authors.lastname: Haeufle
authors.affiliation: Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Germany and Friedrich Schiller Universität, Institut für Sportwissenschaft, Seidelstrasse 20, D-07743 Jena, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Günther
authors.affiliation: Universität Stuttgart, Institut für Theoretische Physik 1, Pfaffenwaldring 57, D-70550 Stuttgart, Germany.
authors.forename: G
authors.initials: G
authors.lastname: Wunner
authors.affiliation: Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Germany and Universität Stuttgart, Stuttgart Research Centre for Simulation Technology (SRC SimTech), Pfaffenwaldring 5a, D-70569 Stuttgart, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Schmitt
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003491:Cybernetics / Q000379:methods; D019277:Entropy; D025461:Feedback, Physiological / Q000502:physiology*; D006801:Humans; D016247:Information Storage and Retrieval / Q000379:methods; D008954:Models, Biological; D015233:Models, Statistical; D009068:Movement / Q000502:physiology*; D009119:Muscle Contraction / Q000502:physiology*; D018482:Muscle, Skeletal / Q000502:physiology*; D005082:Physical Exertion / Q000502:physiology*; D012371:Robotics / Q000379:methods