The Kinematics of Hyper-Redundant

This paper considers the kinematics of hyper- redundant (or "serpentine") robot locomotion over uneven solid terrain, and presents algorithms to implement a variety of "gaits." The analysis and algorithms are based on a continuous backbone curve model which captures the robot's macroscopic geometry. Two classes of gaits, based on stationary waves and traveling waves of mechanism deformation, are introduced for hyper-redundant robots of both constant and variable length. We also illustrate how the locomotion algorithms can be used to plan the manipulation of objects which are grasped in a tentacle-like manner. Several of these gaits and the manipulation algorithm have been implemented on a 30 degree-of-freedom hyper-redundant robot. Experimental results are presented to demonstrate and validate these concepts and our modeling assumptions. over uneven terrain. These gaits are based on stationary and traveling waves of mechanism deformation, and have analogues in inchworm and caterpillar locomotion and the creeping gaits of snakes. These gaits are largely "kinematic" in nature. That is, dynamic effects and a detailed model of the friction between the mechanism and the ground are not critical to the function or understanding of these gaits at reasonable speeds. In contrast, dynamic effects, the internal distribution of mechanism forces, and a frictional model are important for some gaits, such as those which are analogous to the undulatory and concertina gaits used by snakes. Hence, the analysis in this paper does not cover all possible hyper- redundant robot gaits. The gaits considered in this paper were chosen for their simplicity, implementability, and wide range of applicability. Further, we show how these locomotion algorithms can be used to implement a novel scheme for planning the manipulation of objects which are grasped in a tentacle-like fashion. The gait algorithms are based on a "backbone curve" mod- eling technique that was introduced in earlier works devoted to hyper-redundant manipulator kinematics, trajectory planning, and obstacle avoidance (5), (4), (8). With the backbone curve abstraction, surprisingly simple ideas and mathematics can be used to understand and implement relatively complicated hyper-redundant robot locomotion phenomena. Several of the gaits and the object manipulation scheme have been im- plemented in a 30 degree-of-freedom hyper-redundant robot prototype, and experimental results are also presented to show that the algorithms are indeed able to be implemented.