Straight Worms under Adaptive Control and Friction - Part 1: Modeling

This paper is a contribution to the adaptive control of worm-systems, which are inspired by biological ideas, in two parts. We introduce a certain type of mathematical models of finite DOF worm-like locomotion systems: modeled as a chain of

k

interconnected (linked) point masses in a common straight line (a discrete straight worm).We assume that these systems contact the ground via 1) spikes in Part 1 and then 2) stiction combined with Coulomb sliding friction (modification of a Karnopp friction model) in Part 2. We sketch the corresponding theory. In general, one cannot expect to have complete information about a sophisticated mechanical or biological system, only structural properties (known type of actuator with unknown parameters) are known. Additionally, in a rough terrain, unknown or changing friction coefficients lead to uncertain systems, too. The consideration of uncertain systems leads to the use of adaptive control in Part 2 to control such systems. Gaits from the kinematical theory (preferred motion patterns to achieve movement) in Part 1 can be tracked by means of adaptive controllers (

λ

-trackers) in Part 2. Simulations are aimed at the justification of theoretical results.