Passive Dynamics Research Of One-Legged Hopping Robots

One-legged hopping robot can adapt to the needs of different terrain, effectively complete various tasks for human. Its passive dynamic motion planning is proposed to better achieve energy efficiency of one-legged hopping robot. In a state of passive dynamic movement, its energy consumption will be greatly reduced. In order to find one-legged hopping robot's passive dynamics periodic trajectories, many scholars took the simplest SLIP-modeled one-legged hopping robot as the object, and then analyzed respectively in approximate analytical and numerical methods. The results show that there is still no perfect method for the analysis of the general one-legged hopping robot, which is belong to the hybrid systems, the deviation of its solution can be so sensitive that more accurate solutions are needed to achieve its passive dynamic periodic motion planning.Based on the above, this paper proposes a complete set of numerical algorithms for periodic motion planning of the hybrid nonlinear dynamic systems. First of all, the approximate optimal value of the initial state can be acquired by using simulated annealing algorithm, and then this optimal value was taken as the initial value of the numerical iteration algorithm. In the iteration algorithm, the periodic motion is transformed into the solution of the fixed points on the Poincare crossing by Poincare mapping, so its numerical solution can be acquired by Newton-Raphson algorithm.To show the complexity of the hybrid nonlinear dynamic systems, Van der Pol equation, Duffing equation and Alpazur oscillator are taken for instance. Those rich dynamic characteristics are gradually revealed by the corresponding numerical algorithms, also the time parameters needed to focus on in numerical solution are bring forward and a general solution is given. The proposed numerical algorithm is applied to the passive dynamic analysis of SLIP-modeled one-legged hoping robot system, and the desired results are achieved. An object function, which is used to solve the approximate optimal value of the initial state of system, is extracted on the energy loss by division of the robot's periodic orbit. Through a series of Poincare maps 8-dimensional continuous space can be reduced into discrete 7-dimensional space, then the fixed point on the corresponding Poincare section is solved by Newton-Raphson algorithm. Finally, the passive dynamic periodic orbit under some conditions is found via a simulation, also the energy efficiency is discussed.At last, a number of ideas in the next step of work plan are made, which aim to the passive dynamics of the non-SLIP-modeled one-legged hopping robot.