Continuous-time update laws with radial basis step length for control of bipedal locomotion

Presented is a novel approach for designing continuous-time update laws to update the parameters of stabilising controllers during continuous phases of bipedal walking such that (i) a general cost function, such as the energy of the control input over single support, can be minimised in an online manner, and (ii) the exponential stability of the corresponding limit cycle for the closed-loop impulsive system is not affected. Formally, a class of update laws with a radial basis step length is developed to minimise a cost function in terms of the stabilising controller parameters and initial states of the mechanical system.