Modeling And Design Of Dynamic Walking Control Strategy For Under-actuated Biped Robot

Biped robot is one of the most important fields of humanoid robotics, having much significance in academic research and actual application. But the biped robot is a complex mechanical system with multi-degree of freedom, and the dynamics modeling, gait analysis and walking control strategy synthesis are difficult tasks. Biped machine with high stability and efficiency and the principle of biped walking are the two main topics of researches about biped robot. As for the biped robot prototype, there are many successful ones around the world, but there is still much to be complete to make biped robot be used in practical application. The key reason is that the basic theory of biped walking is still to be improved, to implement biped robot with high stability and low energy consumption. Passive dynamic walking is a new research field of biped robot, aiming to reveal the inherent properties of biped robotic dynamics and principle of stable, robust walking control. The research result can provide much instruction for the mechanical design, periodical gait analysis and calking control synthesis of biped robot.The research of passive dynamic walking was initiated in the last 1980's by T. McGeer. The main topics of research about passive dynamic walking include mechanical design of biped under-actuated robot, walking gait modeling, stability analysis based on periodical orbit and walking control design. Usually used design of under-actuated biped robot has four legs. With specially designed feet with lateral degree of freedom and enable the 3D biped passive dynamic walking along a slope. A passive dynamic walker without actuations can only walk down a slope, but if mounted with some actuations on joints, the robot can walk on level ground. In the mechanical design of under-actuated biped robot, a revolution boom is always used to maintain the lateral balance in walking, and this is also the most usually used method in the design of under-actuated biped.A. Goswami proposed a passive biped model called compass-like biped and gave a summarization of the research about the passive dynamic walking, include gait modeling, analysis, stability properties and dynamic control. The energy based control, learning control are also used in the control of under-actuated biped robot. The virtual constraint control is successfully used in the control of under-actuated walking.The research topic of this thesis is the mechanical design, parameter optimization, and dynamic control strategy design. The main contents, research results and innovative points are presented as follows.Under-actuated biped robot is two legged robot designed under the principle of passive dynamic walking, and has much differences with the full-actuated biped robot in degree of freedom setting, joint actuation and control method. After an exhaustive review of under-actuated biped over the world, the under-actuated biped prototype PADW-JLU II is implemented using the principle of passive dynamic walking to implement high efficient dynamic walking gait. A new design method of adaptive foot with elastic springs is proposed. The new proposed foot structure has a double layer structure and spring between two layers, to make the foot have a lateral rocking degree of freedom. Four spring-rolling wheels are mounted on front and rear side of lower plate, and an extension spring link the top layer plate to the lower leg, making a virtual point foot in the walking of the robot. The new proposed foot design can store the mechanical energy lost in foot collision and reduce the reaction force of the ground. The main aim of the new foot design is to help the robot to maintain the 3D dynamic stability in biped walking.The gait model of under-actuated biped robot is a complex hybrid nonlinear system. The passive gait model of the biped robot is build and the six point of stable walking limit cycle is computed by Newton-Raphson iterative algorithm. Numerical simulation is used to compute the passive gait solution and also the dynamics and energy variation in the gait cycle. The limit cycle on the phase plane does not include time information, then a limit cycle with time dimension information is proposed, making the limit cycle more intuition when display the dynamics of periodic walking gait.The stable walking gait of under-actuated biped is a cyclic orbit and its stability property can be described by Lyapunov stability definition of single state point. The notion of orbital stability is usually used to evaluate the stability of periodic gait cycle. The cyclic orbit and its stability of under-actuated biped robot are defined. Then the local stability of limit cycle based on linearized Poincare map is described and the numerical simulation of Floquet multipliers is presented. The global stability property of limit cycle can be evaluated by its basin of attraction. The basin of attraction is a neighborhood of limit cycle from which the gait trajectory beginning can eventually convergent to the limit cycle, or a cycle trajectory near the limit cycle. The usually used cell mapping method is employed to compute the attraction region of passive walking limit cycles. But the cell mapping method needs a large amount of computation and the accuracy can't be improved much. The cell mapping method is improved by Newton iterative algorithm. The newly proposed method decide the attraction only by computing its boundary using Newton-Raphson iterative algorithm, so much less computation is needed and the accuracy is much higher compared to those of cell mapping method. Using the local and global stability definition of cyclic orbit, the physical parameters of compass-like biped and kneed-biped robot are optimized taking the stability margin as an objective function, to find the best combination of physical parameters and the variation of gait descriptors when the physical parameters vary.The variation of characteristic parameters when slope angle and physical parameters vary is studied by numerical simulations. The period bifurcation and chaotic gait are simulated when the slope angle is large enough. The optimization of slope angle and physical parameters is implemented by local and global stability of passive gait limit cycles. When the local stability is used in the optimization, the maximum Floquet multiplier is used as the norm of local stability for limit cycles. The global stability of limit cycle can be evaluated by the size of attraction region. Because the computation of attraction region is too complicated, the maximum radius of attraction region is proposed as the norm of global stability. The optimization results can be used as an instruction in the mechanical design of under-actuated biped robot. It is also shown that there are some difference between the global stability and local stability of limit cycles under the same physical parameters.The control strategy based on passive dynamic walking principle is one of the most important aims in research of under-actuated biped robot. The notion of limit cycle walking is defined as the walking gait that forms a stable cyclic orbit. The orbital stability and high efficiency is the main properties of this kind of walking gait. The limit cycle based walking gait control is aiming to use the dynamic stability properties of passive dynamic walking limit cycles. The dynamic control strategies of kneed-passive dynamic walkers are studied, such as the energy base control and the slope invariant control. At last, a dynamic control based on learning control is developed using the principle of limit cycle walking. The passive dynamic walking gait is regarded as the reference trajectory and PD control is used to make the state of robot converge to the reference limit cycle. The PD parameters are learned and optimized by the dynamic response. Simulation experiments show the validity of the proposed method. The robot can start from still and eventually converge to the reference limit cycle.