Application of phase-plane method in generating minimum time solution for stable walking of biped robot with specified pattern of motion

Walking with a maximum speed is an interesting subject in the field of biped motion. Giving an answer to the question of what is the maximum achievable speed of a certain biped walking with a physically acceptable pattern? is the main objective of this work. In this paper, minimum time motion of biped was studied during one step that consists of single support phase (SSP) and double support phase (DSP). The minimum time problem is formulated with stability and non-slip conditions along with actuator limits expressed as some inequality constraints. In addition, certain kinematic constraints in terms of hip joint position are considered that ensure an acceptable walking pattern. A phase-plane technique is used to find the minimum time solution. A numerical simulation is given to shed some light on how the proposed method works. Validity and effectiveness of the method are verified by comparing the results with those of other researches.