Controlling a system with redundant degrees of freedom. I. Torque distribution in still standing stick insects

Levy J, Cruse H. Controlling a system with redundant degrees of freedom. I. Torque distribution in still standing stick insects. Journal of Comparative Physiology A. 2008;194(8):719-733.The question is investigated as to how a stick insect solves the task of distributing its body weight onto its six legs, i.e., how are the torques coordinated that are produced by the 18 joints (3 per leg). Three-dimensional force measurements of ground reaction forces have been used to calculate the torques developed by each of the 18 joints. Torques were found to change considerably although the body and the legs of the animal did not move. This result implies a tight cooperation between the 18 joint controllers. Indeed, in each individual experiment, strong correlations could be observed between specific pairs of joints. However, in spite of thorough analysis, no general correlation rules between torques could be detected. The only common attribute found for all experiments was that high absolute torques observed at the beginning of the experiment tend to converge to some minimum over time. Thus, the insects tend to decrease the torques while standing still, but do not use fixed rules. Rather they appear to exploit their extra degrees of freedom and produce time courses that can strongly vary between experiments. Possible mechanisms underlying this behaviour are discussed in a companion paper [Levy and Cruse (2008) Controlling a system with redundant degrees of freedom: ii. solution of the force distribution problem without a body model, submitted]