Underactuated Robot Gait Optimization And Stability Control

The research on biped underactuated walking robot has important theoretical andpractical values, which has drawn extensive attention from scholars around the world.Nowadays there has been a great development of research on fully-actuated bipedrobot, which still can’t meet the demands of people. The reasons are mainly highenergy consumption and low efficiency. The pure underactuated biped walking robotcan achieve the highly efficient and stable single walking gait by taking advantage ofthe effect of the gravity potential. But the walking of robot can only be applied on theslope without the driving power, and the superior stability can’t be sustained. Therobot walking by adopting the passive pattern has the merit of light weight, energysaving and being used on any slope and so on. The research on the underactuatedwalking robot can reveal the intern mechanism of high velocity and efficiency inhuman. The bionic walking control, stability analysis and optimization of the passivebiped walking robot are mainly studied in this paper. The specific content is asfollows:Firstly, the status quo of the underactuated walking robot around the world isreviewed. Then the two dimensional degree and three dimensional degree model ofthe compass-like biped robot and biped robot with knees are respectively constructed.And the dynamic equation of different walking gait is deduced. In order to understandthe injection point of the underactuated driving power of the biped robot, analyzingthe process of change of the muscle electrical signal when human is walking can helpus realize that the ankle plays a crucial role in human biped walking. Hence thedriving torque of the biped walking robot comes from the ankle joint in this paper.The time scaling control is brought forward, which can realize the adjustment ofthe walking speed. The feasibility of this control suitable for the continuous system isanalyzed in the hybrid system of the biped robot. Moreover, that the time scalingcontrol and virtual gravity control are equivalent is testified. Taking simulationresearch into the constant time scaling and varable time scaling control of the compassrobot and the robot with knees verifies that the time scaling control can achieve the fast switch between any gaits.The energy shaping control is proposed, which realizes the simultaneouslychange of the walking speed and gait length of the biped walking robot. Because thatthe matching condition of the energy shaping control is the partial differentialequation, in order to simplify the solution to energy shaping controller, the nonlinearpartial differential equation is transformed into the linear partial differential equationby introducing the kinetic energy inner product theory. The compass-like biped robotonly driving the ankle joints is taken for example to achieve the kinetic energyshaping controller and to testify the simulation of the compass-like robot and the robotwith knees. So as to broaden the walking range, the control strategy combining theinvariable angle control and energy shaping control is introduced, which apparentlyimproves the robustness. Simultaneously the energy shaping control is beingexpanded to the three dimensional system of the biped walking robot. By constructingthe almost-cyclic lagrangians function and taking advantage of the constraintconditions, the forward walking and lateral movement decoupling is realized.That the underactuated biped robot system has the passivity is analyzed andtestified by making use of the passivity theory. From the viewpoint of energy, thelyapunov function is built to verify the stability of energy shaping control and toachieve the biped robot walking in a wide range stably. According to the distributionof the walking state space, the sub-section control is applied. Based on the dimension,the available state and the natural domain of attraction of the robot, the state space isdivided into different sections. Taking different control strategies according todifferent sections can realize the robot stably walking in a wide range.The gait optimal control problem is taken into research by taking thecompass-like biped robot for example. In order to solve the optimal problem of thehybrid dynamic system, Pontryagin extremum theory is applied and the constraintfunction and penalty function are introduced. Hence the solution to the optimalcontrol of the two boundary values is simplified, and the optimal control torque andstate are achieved.