欠驱动步行机器人运动学机理与控制策略研究
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摘要
本文主要研究了欠驱动步行机器人被动行走步态的内在机理,并开发了Compass-like双足步行机器人的稳定行走控制策略。建立了Compass-like双足步行机器人被动行走步态的数学模型,开发了相应的软件仿真平台,分析了被动行走步态中的能量转化关系,进一步研究了参数变化时被动行走步态动态特性的变化规律。设计并实现了被动行走步态的基本控制算法,包括能量控制,角度不变控制,基于能量的角度不变控制,扩大了被动行走步态极限环的收敛域,增强了行走步态的稳定性与抗干扰性能。通过仿真分析了机器人被动行走的分叉、混沌步态及其产生的原因,提出了混沌步态新的动力学模型,并应用脉冲控制方式实现了机器人混沌运动的稳定控制。模仿人类行走步态双腿运动的对称性,提出了Compass-like双足步行机器人的反向同步控制方法,实现了机器人双腿对称行走步态,通过机器人机械能的反馈控制,实现了对机器人平均前进速度的控制。为了实现欠驱动双足被动机器人能够实现复杂环境中的高效稳定行走步态与复杂的姿态控制,借鉴人类行走过程中的多模式控制方法,提出了欠驱动步行机器人的分域控制方法,并以Compass-like双足步行机器人为对象进行了具体的分域控制算法设计与实现,仿真结果验证了算法的有效性。分域控制算法把稳定行走步态极限环作为控制的目标轨迹,能使机器人产生新的稳定行走步态,大大提高机器人行走的稳定性与抗干扰性,为被动机器人复杂控制算法的设计提供了良好的解决思路。本文的一系列理论研究工作,着眼点在于从理论上研究被动行走步态动态特性及其控制策略开发,对仿人形双足机器人机构设计创新和机器人行走的高效鲁棒控制策略的开发具有一定的借鉴与指导意义。
The study on humanoid-robotics is the most advanced direction in the field of robotics research, during the past twenty years, some universities as well as some distinguished laboratories in the world have paid more attention to the research of this field and have finished some well-known workable models machine, in addition these typical models have great impact on the society and have changed our lives in some field greatly. Also the study on the passive gait biped has attracted so many researchers and it has gradually become the focus of the advanced robotics research.
The notion that it is possible to achieve walking gaits from mechanical bipeds powered only by gravity has been proposed since the pioneering work of McGeer in the early 1990’s. Several researchers, such as M.W.Spong, A.Goswami and M.Garcia have also studied compass-like gait biped robot theoretically and have made some great progresses. The theory so-called“passive gait biped”may help to explain the efficiency, stability as well as the robustness of human locomotion and also it can provide some brand-new insight into the design of the walking robots and with it to design some more realistic robotics. In addition, the study of the special impulsive shoes for the robots, the design of the coupled ideal legs, the design of the bio-mechanical legs, the industrialization of the assistant walking legs utilizing the property of human are all the excited directions of the research and the further study of all those which have been talked above will meet the brilliant future. On the basis of the passive dynamics as well as availing the self-adjust function of human’s own property, we may have finished the design of some more practical, convenient and low-energy cost auxiliary walking mechanics. The main idea of the passive dynamics is: to begin with, propose some appropriate passive gait biped model, then establish the corresponding mathematical descriptions of this walking model, in spite of this, to give the analysis of the dynamical property and walking characteristics, and also the arithmetic control strategies to reveal the internal theory of human’s high speed and the high efficiency gait biped walking.
The gait biped model of the humanoid robotics contains the typical rimless axis model, two points gait biped model, compass gait biped and planar five links lever model, etc. The rimless axis model is the original gait biped mechanics, and the paper has analyzed the dynamical properties and mathematical descriptions of this kind of mechanics, the model is very simple and can produce some humanoid gaits, so the deduction of the equation can involve the problems of the calculation of the initial value, the bifurcation of the gaits, the variable selection of the mechanic equations, the paper has done some beneficial works in the field.
The focus of the paper is a relative further study of the passive gait of a compass-like, planar, biped robot on inclined slopes. Comparing with the double-leg mass robot, the new model has paid some consideration on the aspect of mass distribution of the robot and the process of the discussion and the analysis on the bipedal robots are much more complex with the much less assumption, that is to say, the new model can reveal the real human-like walking in great degree. The robot is kinetically equivalent to a double pendulum, possessing two knee-less legs with point masses and a third point mass at the“hip”joint with the two processes of swing stage and instantaneous collision stage, different methods are needed for the different walking stage. For the mathematical model of the bipedal gait is a hybrid dynamical equation with the property of advanced derivation, nonlinearity and strong coupled. So some traditional methods will be of no function and the analysis of Poincare method has been used here. Phase-space limit cycle of a symmetric gait of the robot, the conversion law between kinetic energy and potential energy, the energy distribution between the swing leg and stance leg during the walking process have been presented in detail and in spite of this, the paper also has a discussion about culmination points which exist in potential and kinetic energy conversion of the coupling two legs. The simulation result just captures the entire evolution of the gait on any given slope and also the new method of combining the Poincare idea and digital simulation have been brought out to explain the stability as well as some special character of the limit cycle that interest us corresponding to the different slope. With the change of the slope, there will exist some state of the gait limit cycle such as stable gait, bifurcation, approximate chaos gait and chaos gait. The problem of initial value to the stable gait cycle is one of the most difficult events to the study of this research, in spite of this, the database of the initial value has been set up and some energy property as well as the property of coupled legs has been discussed in detail. Many of the consequences of the study have been considered to transplant to the real robots production, all the research above will have realistic significance in helping us to be better aware of walking rules and global properties of the biped gaits of the robot.
In spite of the analysis talking above, the paper also focuses on the analysis of the behavior of symmetric and asymmetric passive gaits using a simple nonlinear biped model and continues the investigation into the control of the compass gait biped. Three parameters, namely the ground slope angle, and the mass ratio and length ratio of the robot are used here to observe the target gait property to improve the robot performance as well as generating new gaits. In response to a continuous change in any one of these three parameters, the symmetric and steady gait of the passive robot will gradually evolve through a regime of stable gait, period-doubling bifurcation, and eventually arriving at an apparently chaotic gait. The control law presented here will drive the chaotic gait back to the original stable one; some chaotic control strategies as well as the damper that increases gait stability have been discussed in detail. All the control strategies are presented here such as the control idea based on energy control, the slope invariance control, the slope invariance control combining with energy control and also based on the average speed with energy control, the sub-section control, chaos gait control, and impulsive control in the base etc. Some basic control strategies on the passive compass gait biped, with controller added at the hip and at the ankle respectively following the compass-like, planar, biped robot model on inclined slopes, have been addressed here as the energy based control law, with the use of the hip and ankle control respectively, to attain to the reference energy of certain limit cycle more efficiently than that without control and also attain to any target limit cycle we expect within some region. In addition, we analyzes the global control property on the robots in detail and moreover a comparison between the simply ankle and hip control respectively has been discussed. The so called energy based control slope invariance law and also a specified average speed of progression control law have been discussed respectively in detail. Both control strategies are on the basis of potential energy shaping control. The specified average speed of progression control law will gain the advantage in establishing the relationship between the average speed of progression and the target energy to improve the robot performance as well as generating new gaits. While the energy based control slope invariance law will get away from the limit assumption that for the given slope a passive limit cycle exists and have already been identified. All these control laws will increase not only the exponential rate of convergence to the limit cycle but also its basin of attraction in different aspect and these have increased the robustness of the closed loop system to external disturbances and variation in the ground slope greatly. Symmetry property typical of healthy gait in human walking has been applied into the design and analysis on the compass-like biped model as to explicitly explain the efficiency of human and animal locomotion. Some new control strategy of“anti-phase synchronization”has been presented here, with the new presumption of the collision model, to reduce the complexity such as the property of nonlinearity and strong coupling between two legs of this hybrid dynamic system. A controller which is able to solve the synchronization problem in such a way that the pendulum reaches the desired level of energy and they move synchronously in opposite directions has been introduced. In addition, the discussion to the construction of new Lyapunov function and simulation results have just proved the validity of the strategy. The method stated rightly above in the paper is helpful to practical application of the design of the robot’s gait. To the best of our knowledge, it is the first time to introduce the concept of synchronization to explain and control the motion of passive biped theoretically. Some research so called”sub-sectional control”to attain to the goal of keeping overall state-space stable control of the compass gait biped is another way that will be of great help to the control of bipedal robots, enabling the robot to adapt to the different ground such as up and down-wards as well as the flat. The paper finishes the design of PD controller as the transition controller with the use of tracking the optimal human-like and efficient gaits; and also some domain controller, of which the function of realizing the smooth switch among various domain regions has been presented here with the estimation of the attraction region as well as the transition boundary. The result of the paper will help to find an important practical application in the design of the robot’s gait. This will greatly increase the robustness of the closed loop system to external disturbances and variation in the ground slope attaining the goal of mimicking the gait of human-walking. To the best of our knowledge, it is the pioneering work to introduce the basic concept and also the implementation of the method on sub-sectional control to explain and control the motion of passive biped theoretically. The research will do some favor to the theory of ZMP(zero movement point), which is a kind of traditional control strategy to the energy based walking robots, though the idea will realize the actual walking of the robots, while it will meet some difficulty in explaining the internal control law of the tracking law and will lose its function when the walking gaits are outside the region of ZMP stability theory. The method proposed above will be helpful to the investigation of the features of the latent behavior of the robot gait and will demonstrate the existence and the stability of symmetric and asymmetric passive gaits.
For the sake of further experimental research, the paper also presents some documents concerning the simulation of the passive gait biped, some initial value database has been established to tackle the problem of gait biped, in addition, the paper also adopts the idea of V style to finish the study of ECU controller, constitutes the act from the initiation, experiment to production, the conclusion will be applicable when used in a kind of seven degree robot practical model with the up-body and knees.
From what we have discussed above, we may safely draw the conclusion that some basic researches on the study of passive gait biped, both on theoretic and application, have been given in the paper, some of them are the pioneering work of this field, the work of the paper will be of certain importance and also some guidance to the researchers.
The study on humanoid-robotics is the most advanced direction in the field of robotics research, during the past twenty years, some universities as well as some distinguished laboratories in the world have paid more attention to the research of this field and have finished some well-known workable models machine, in addition these typical models have great impact on the society and have changed our lives in some field greatly. Also the study on the passive gait biped has attracted so many researchers and it has gradually become the focus of the advanced robotics research.
The notion that it is possible to achieve walking gaits from mechanical bipeds powered only by gravity has been proposed since the pioneering work of McGeer in the early 1990’s. Several researchers, such as M.W.Spong, A.Goswami and M.Garcia have also studied compass-like gait biped robot theoretically and have made some great progresses. The theory so-called“passive gait biped”may help to explain the efficiency, stability as well as the robustness of human locomotion and also it can provide some brand-new insight into the design of the walking robots and with it to design some more realistic robotics. In addition, the study of the special impulsive shoes for the robots, the design of the coupled ideal legs, the design of the bio-mechanical legs, the industrialization of the assistant walking legs utilizing the property of human are all the excited directions of the research and the further study of all those which have been talked above will meet the brilliant future. On the basis of the passive dynamics as well as availing the self-adjust function of human’s own property, we may have finished the design of some more practical, convenient and low-energy cost auxiliary walking mechanics. The main idea of the passive dynamics is: to begin with, propose some appropriate passive gait biped model, then establish the corresponding mathematical descriptions of this walking model, in spite of this, to give the analysis of the dynamical property and walking characteristics, and also the arithmetic control strategies to reveal the internal theory of human’s high speed and the high efficiency gait biped walking.
The gait biped model of the humanoid robotics contains the typical rimless axis model, two points gait biped model, compass gait biped and planar five links lever model, etc. The rimless axis model is the original gait biped mechanics, and the paper has analyzed the dynamical properties and mathematical descriptions of this kind of mechanics, the model is very simple and can produce some humanoid gaits, so the deduction of the equation can involve the problems of the calculation of the initial value, the bifurcation of the gaits, the variable selection of the mechanic equations, the paper has done some beneficial works in the field.
The focus of the paper is a relative further study of the passive gait of a compass-like, planar, biped robot on inclined slopes. Comparing with the double-leg mass robot, the new model has paid some consideration on the aspect of mass distribution of the robot and the process of the discussion and the analysis on the bipedal robots are much more complex with the much less assumption, that is to say, the new model can reveal the real human-like walking in great degree. The robot is kinetically equivalent to a double pendulum, possessing two knee-less legs with point masses and a third point mass at the“hip”joint with the two processes of swing stage and instantaneous collision stage, different methods are needed for the different walking stage. For the mathematical model of the bipedal gait is a hybrid dynamical equation with the property of advanced derivation, nonlinearity and strong coupled. So some traditional methods will be of no function and the analysis of Poincare method has been used here. Phase-space limit cycle of a symmetric gait of the robot, the conversion law between kinetic energy and potential energy, the energy distribution between the swing leg and stance leg during the walking process have been presented in detail and in spite of this, the paper also has a discussion about culmination points which exist in potential and kinetic energy conversion of the coupling two legs. The simulation result just captures the entire evolution of the gait on any given slope and also the new method of combining the Poincare idea and digital simulation have been brought out to explain the stability as well as some special character of the limit cycle that interest us corresponding to the different slope. With the change of the slope, there will exist some state of the gait limit cycle such as stable gait, bifurcation, approximate chaos gait and chaos gait. The problem of initial value to the stable gait cycle is one of the most difficult events to the study of this research, in spite of this, the database of the initial value has been set up and some energy property as well as the property of coupled legs has been discussed in detail. Many of the consequences of the study have been considered to transplant to the real robots production, all the research above will have realistic significance in helping us to be better aware of walking rules and global properties of the biped gaits of the robot.
In spite of the analysis talking above, the paper also focuses on the analysis of the behavior of symmetric and asymmetric passive gaits using a simple nonlinear biped model and continues the investigation into the control of the compass gait biped. Three parameters, namely the ground slope angle, and the mass ratio and length ratio of the robot are used here to observe the target gait property to improve the robot performance as well as generating new gaits. In response to a continuous change in any one of these three parameters, the symmetric and steady gait of the passive robot will gradually evolve through a regime of stable gait, period-doubling bifurcation, and eventually arriving at an apparently chaotic gait. The control law presented here will drive the chaotic gait back to the original stable one; some chaotic control strategies as well as the damper that increases gait stability have been discussed in detail. All the control strategies are presented here such as the control idea based on energy control, the slope invariance control, the slope invariance control combining with energy control and also based on the average speed with energy control, the sub-section control, chaos gait control, and impulsive control in the base etc. Some basic control strategies on the passive compass gait biped, with controller added at the hip and at the ankle respectively following the compass-like, planar, biped robot model on inclined slopes, have been addressed here as the energy based control law, with the use of the hip and ankle control respectively, to attain to the reference energy of certain limit cycle more efficiently than that without control and also attain to any target limit cycle we expect within some region. In addition, we analyzes the global control property on the robots in detail and moreover a comparison between the simply ankle and hip control respectively has been discussed. The so called energy based control slope invariance law and also a specified average speed of progression control law have been discussed respectively in detail. Both control strategies are on the basis of potential energy shaping control. The specified average speed of progression control law will gain the advantage in establishing the relationship between the average speed of progression and the target energy to improve the robot performance as well as generating new gaits. While the energy based control slope invariance law will get away from the limit assumption that for the given slope a passive limit cycle exists and have already been identified. All these control laws will increase not only the exponential rate of convergence to the limit cycle but also its basin of attraction in different aspect and these have increased the robustness of the closed loop system to external disturbances and variation in the ground slope greatly. Symmetry property typical of healthy gait in human walking has been applied into the design and analysis on the compass-like biped model as to explicitly explain the efficiency of human and animal locomotion. Some new control strategy of“anti-phase synchronization”has been presented here, with the new presumption of the collision model, to reduce the complexity such as the property of nonlinearity and strong coupling between two legs of this hybrid dynamic system. A controller which is able to solve the synchronization problem in such a way that the pendulum reaches the desired level of energy and they move synchronously in opposite directions has been introduced. In addition, the discussion to the construction of new Lyapunov function and simulation results have just proved the validity of the strategy. The method stated rightly above in the paper is helpful to practical application of the design of the robot’s gait. To the best of our knowledge, it is the first time to introduce the concept of synchronization to explain and control the motion of passive biped theoretically. Some research so called”sub-sectional control”to attain to the goal of keeping overall state-space stable control of the compass gait biped is another way that will be of great help to the control of bipedal robots, enabling the robot to adapt to the different ground such as up and down-wards as well as the flat. The paper finishes the design of PD controller as the transition controller with the use of tracking the optimal human-like and efficient gaits; and also some domain controller, of which the function of realizing the smooth switch among various domain regions has been presented here with the estimation of the attraction region as well as the transition boundary. The result of the paper will help to find an important practical application in the design of the robot’s gait. This will greatly increase the robustness of the closed loop system to external disturbances and variation in the ground slope attaining the goal of mimicking the gait of human-walking. To the best of our knowledge, it is the pioneering work to introduce the basic concept and also the implementation of the method on sub-sectional control to explain and control the motion of passive biped theoretically. The research will do some favor to the theory of ZMP(zero movement point), which is a kind of traditional control strategy to the energy based walking robots, though the idea will realize the actual walking of the robots, while it will meet some difficulty in explaining the internal control law of the tracking law and will lose its function when the walking gaits are outside the region of ZMP stability theory. The method proposed above will be helpful to the investigation of the features of the latent behavior of the robot gait and will demonstrate the existence and the stability of symmetric and asymmetric passive gaits.
For the sake of further experimental research, the paper also presents some documents concerning the simulation of the passive gait biped, some initial value database has been established to tackle the problem of gait biped, in addition, the paper also adopts the idea of V style to finish the study of ECU controller, constitutes the act from the initiation, experiment to production, the conclusion will be applicable when used in a kind of seven degree robot practical model with the up-body and knees.
From what we have discussed above, we may safely draw the conclusion that some basic researches on the study of passive gait biped, both on theoretic and application, have been given in the paper, some of them are the pioneering work of this field, the work of the paper will be of certain importance and also some guidance to the researchers.
引文
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