Modeling and Optimal Control of Human-Like Running

Designing and controlling an anthropomorphic mechatronic system that is able to perform a dynamic running motion is a challenging task. One difficulty is that the fundamental principles of natural human running motions are not yet fully understood. The purpose of this paper is to show that mathematical optimization is a helpful tool to gain this insight into fast and complex motions. We present physics-based running motions for complex models of human-like running in three dimensions that have been generated by optimization. Running is modeled as a multiphase periodic motion with discontinuities, based on multi-body system models of the locomotor system with actuators and spring-damper elements at each joint. The problem of generating gaits is formulated as offline optimal control problem and solved by an efficient direct multiple shooting method. We present optimization results using energy-related criteria and show that they have a close resemblance to running motions of humans. The results provide information about the internal forces and torques required to produce natural human running, as well as on the resulting kinematics.