Adaptive internal impedance control for stable walking on uncertain visco-elastic terrains

This paper investigates how a walker could maintain the variability of an arbitrary set of state variables within desired margins while walking on an uncertain soft terrain. The state variables are dynamically related to the visco-elastic impedance parameters of the body on a given set of uncertain soft terrains using internal memory primitives. A rimless wheel, a walker in its simplest form, is used to perform numerical simulations based on analytical dynamic models and hardware experiments to test a novel algorithm. The rimless wheel model is widely used by the legged locomotion research community to understand basic collision and energetics during passive dynamic walking. Very often, variability of punctuated force perturbations across collisions between the legs and the ground cause uncertain steady state dynamics of walking. This leads to the existence of a finite probability that certain state variables can reach unstable regions. Such phenomenon is known as metastability of walking. In this case, we actuate the rimless wheel with a constant torque leaving it to develop any speed profile for a given visco-elastic impedance distribution of the ground and its own vertical visco-elastic impedance that pushes the rimless wheel against the ground. Here we measure the robustness of the novel algorithm by its ability to shift the distribution of collision forces to a safer region in order to minimize the probability of reaching a given critical force threshold. Our analysis shows that the generalization of the variability of walking in different regions of the internal and external visco-elastic impedance spaces can simplify the computational challenges of robust walking on uncertain visco-elastic terrains.