A Framework for Modeling Closed Kinematic Chains with a Focus on Legged Robots

This paper presents the foundations of a MATLAB framework for dynamic modeling and simulation of closed kinematic chain (CKC) mechanisms, with a particular focus on implementation with legged locomotive mechanisms. As such, the framework supports both floating-base and fixedbase systems. Through the use of singular perturbation theory, various CKC mechanisms can be modeled so that constraint errors asymptotically converge to zero, thus avoiding the numerical drift that plagues commonly used methods. A functional API and the relevant core commands necessary to construct a model are presented. Two robotic legs incorporating CKC mechanisms are utilized as case studies, and simulations of each leg performing a dynamic monopedal gait are illustrated.