Research The Gait Stability Of Hopping Kangaroo Robot Based On Spring-mass Model

With the bionic robot developing in these fields which adapt the unstructured and unknown environment, and complete various complex works flexibly and reliably, settling the motion stability of bionic robot has become the key problem and frontal topic. Therefore, based on the fundamental of bionic robot's motion stability and analysing the characteristics of kangaroo's leaping motion, this paper established the simplified system model of hopping kangaroo robot and analyzed the gait stability of leaping motion.First of all, on the base of referring dozens of references of bionic robotics' motion stability home and abroad, this paper summarized the present status of the research on the theory and method of bionic robotics' motion stability, and generalized the developing directions. And the research work in this paper, including researching the motion features, leaping motion characteristics and force characteristics of kangaroos, supplied the necessary foundation for the model building and analysis.Next, based on the characteristics of the kangaroos hopping, the spring-mass model of hopping kangaroo robot was developed. The dynamic equation was established using Lagrange method and linear approximation, and the radial motion and horizontal motion during stance phase were analysed. According to gait stability conditions, the apex return map function, existence of fixed point and stability of fixed point of hopping kangaroo robot were studied, the range of each parameter which satisfied the gait stability during kangaroo robot hopping process and the explicit relational expression of parameters were obtained, and the variable relations of parameters which kangaroo robot hopped stably were obtained and the linear approximation analysis was proved to be effective by example. The analytic result indicates that the hopping kangaroo robot can keep continuous hopping gait stability when existence of fixed point and the dimensionless energy E_s≥2, spring stiffness coefficient k ≥ 0.5 kN/m, touchdown angle α₀ ≥ 37°.Finally, considering the moment effect of kangaroo's ankle joint, the spring andtwo-mass model of hopping kangaroo robot was established. The critical conditions ofupper and lower boundary stability indices of stable region which satisfied the gait stability when hopping kangaroo robot in stance were gained by using energy method, and the dynamic stable region was gained by Matlab, at the meantime, the span and variable relations of parameters which satisfied the dynamic stable region were gained. The analytic result proves that for a 6.6kg of hopping kangaroo robot, it can keep stability in stance when the hopping velocity ve [0.2,2] m/s, spring stiffness coefficientk e [0.01,1.36]kN/m, touchdown anglea0 e [18°,75°].This paper is the theory foundations for increasing the performance design and controlling the leaping motion of kangaroo robot.