Feedback Control for Natural Oscillations of Locomotion Systems Under Continuous Interactions With Environment

We consider a class of multibody robotic systems inspired by dynamics of animal locomotion, such as swimming and crawling. Distinctive properties of such systems are that the stiffness matrix is asymmetric due to skewed restoring force from the environment, and the damping matrix is a scalar multiple of the inertia matrix when the body is flat like those of fish. Extending the standard notion to this class, we define the natural oscillation as a free response under the damping compensation to yield marginal stability. The natural oscillation of the body provides a basic gait for locomotion. We propose a class of simple nonlinear feedback controllers to achieve entrainment to the natural oscillation of the body, resulting in a prescribed average velocity. As an example, a link chain system with symmetric mechanical structure is considered, and its natural oscillation is shown to exhibit traveling waves appropriate for undulatory locomotion. Controllers are designed under various conditions to achieve prescribed locomotion speeds by natural oscillations. In particular, it is shown how design parameters can be chosen to increase the rate of convergence, and how the locomotion speed can be set by adjusting the natural frequency through body stiffness compensation.