Modeling bipedal locomotion trajectories using hybrid automata

Modelling the joint trajectories of a biped locomotion correctly is a highly challenging problem due to the complex nature of biped locomotion. In human as well as in biped humanoids the periodic walking pattern which is known as gait, consists of both discrete (known as stance phase) and continuous phases (known as swing phase). The system is highly nonlinear and modelling using conventional kinematics has not proved to be very effective. Several compelling assumptions to make model simple makes it unrealistic. In this research work we present a computational model for prediction, formal verification and analyses of joint trajectories of bipedal locomotion using powerful theoretical computer science framework which is known as automata theory-more precisely here hybrid automata technique has been used for modelling. We argued that hybrid automata is more suitable to model a biped locomotion which is inherently hybrid (consisting of discrete and continuous phases) in nature. One of the major contributions of the paper is developing the hybrid automata model for automatic generation of joint trajectories for different sub phases of a bipedal gait. Other contributions include the development of generic equations for seven sub interval phases of a gait cycle which has been divided into eight equal parts and verification of its correctness by comparing the model with one existing standard model of OpenSim named as GAIT -2354 [1]. Through rigorous simulations we have established that the hip and knee joint trajectories generated by our hybrid automata based model closely matches with OpenSim model and that of captured data driven model of normal walking. Hence it is effective, robust and generic. We conclude that since the hybrid automata based model has a strong theoretical basis, it can be used for generating hip and knee trajectories for any biped robot for subsequent execution level control.