Adaptive control of a robotic system undergoing a non-contact to contact transition with a viscoelastic environment

Control of a robot interacting with a soft compliant environment is a practically important problem, with potential applications in areas involving human robot interaction (HRI) like rehabilitation, search and rescue, assistive robotics and haptics. The objective, in this paper, is to control a robot as it transitions from a non-contact to a contact state with an unactuated viscoelastic mass-spring system such that the mass-spring is regulated to a desired final position. Because of its simplicity and better physical consistency in explaining the behavior of viscoelastic materials, a Hunt-Crossley nonlinear model is used to represent the viscoelastic contact dynamics. An adaptive Lyapunov based controller is proposed, and shown to guarantee uniformly ultimately bounded (UUB) regulation of the system despite parametric uncertainty throughout the robot and mass-spring systems. The proposed controller only depends on the position and velocity terms, and hence, obviates the need for measuring the impact force and acceleration. Further, the resulting controller is continuous, and the same controller can be used for both non-contact and contact states of the robot with its environment.