基于被动性和欠驱动性的双足机器人运动控制研究
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摘要
双足仿人机器人在环境适应性和人机交互的亲和力等方面具有很大的优势,但利用现有双足运动控制理论和技术实现的双足运动在效率和灵活性上和人类的双足运动相比还有非常大的差距。受人类双足运动的被动性和欠驱动性启发,本文结合了基于被动的控制,能量塑造控制,混杂零动态控制,时间放缩控制等方法,从被动性和欠驱动性的角度研究稳定、灵活、高效的双足运动控制方法。总的来说,本文的研究工作集中在如下几个方面：
首先,针对基于被动的全驱动双足机器人,本文提出结合时间放缩和能量塑造的方法设计对应不同步长和步速的参考轨迹和过渡轨迹,采用反馈线性化的方法设计控制来扩大系统的收敛域,给出了每一步开始时刻更新的控制器条件,使步态响应轨迹和参考轨迹之间的误差渐近地收敛到零。首次从理论上解决了基于被动的全驱动双足机器人变步幅、变步速以及适应复杂环境的稳定行走控制问题,极大地提高了运动的灵活性。
其次,针对考虑欠驱动自由度的双足机器人的平衡站立控制问题,本文利用虚拟完整性约束方法,把机器人驱动关节的角度指定为支撑脚脚板与地面夹角的函数,给出了单脚稳定平衡站立所能承受的外界扰动范围的理论分析方法。当扰动较大,无法实现单脚平衡时,虚拟完整性约束会保证机器人变成双脚支撑状态以避免翻倒,这种扰动下的平衡动作和人非常类似。另外,针对一种特殊的欠驱动平衡站立问题—机器人单脚脚尖平衡站立,本文也首次从理论上给出了虚拟完整性约束设计条件和收敛域估计方法。
再次,针对更一般的欠驱动自由度为一的n自由度的双足机器人,本文首次提出结合时间放缩控制和受控对称性方法来设计统一的反馈控制器,成功实现了欠驱动机器人从一个原始的步态(这个原始的步态既可以是特定斜坡上的一个被动的极限环,也可以是主动控制作用下机器人在地面上产生的一个周期性的行走步态)产生不同斜坡上的周期性步态,并给出了不同斜坡上周期性步态存在性和稳定性的充分必要条件,应用该方法可以极大提高欠驱动双足运动的灵活性和适应性。
最后,本文研究了一种带有储能机构的欠驱动双足机器人的稳定奔跑问题,以其平地上存在的自然的被动奔跑极限环为基础,给出了反馈控制器设计方法,实现水平地面上稳定、节能的奔跑运动。基于文中的控制策略,在理想状态下,奔跑的步态收敛到被动的极限环上之后,系统将没有能量消耗,这一结论对于实现双足机器人高效的类人运动具有重要启示。
针对提出的控制器设计方法,本文在相应的各个章节给出了详细的理论分析,并通过数字仿真进行验证。
Bipedal humanoid robot has a great advantage in adaptability to the environment and strong affinity in human-machine interaction. However, there is a great disparity between bipedal locomotion developed by the existing control theory and real human bipedal loco-motion. Inspired by the passivity and underactuation existing in human bipedal locomotion, this dissertation combines passivity-based control, energy shaping control, hybrid zero dy-namics and time scaling control in order to study stable, agile and efficient locomotion control methods of bipedal robots based on passivity and underactuation. The contribution of this paper can be listed as follows:
Firstly, method combined time scaling control and energy shaping control is proposed for full actuated bipedal robot to construct reference trajectories with different step length and walking speed. A feedback control law is obtained via feedback linearization technique so that the trajectory of the robot converges to a desired passive walking gait. A larger basin of attraction can be obtained. Corresponding feedback control laws are updated at the beginning of each step. Then, the controller condition that the errors measuring the difference of the response trajectory and the reference one asymptotically converge to zero is given. The problem of achieving a stable walking in complex environments for full actuated bipedal robot with regulable step length and walking speed is first solved in this dissertation. The agility of bipedal locomotion is increased.
Secondly, balance control problem of planar bipedal robots with underactuation dur-ing disturbed standing is investigated. Virtual holonomic constraints which specify the an-gles of actuated joints as a function of the rotation angle between the sole of stance foot and ground are introduced. Several conditions guaranteeing the balance of standing for given virtual holonomic constraints arc obtained. Moreover, for a disturbance beyond the bal-ance conditions for single-leg support, robot changes to a double support posture to avoid turnover by the virtual holonomic constraints and this reaction is very human-like. Further, for a special kind of balance:standing on toe which leads to underactuation, the design conditions of virtual holonomic constraints and estimate set of basin of attraction are first given in theory.
Thirdly, a unified feedback control law for n degree-of-freedom biped robots with one degree of underactuation so as to generate periodic orbits on different slopes is first developed in this dissertation. The periodic orbits on different slopes are produced from an original periodic orbit, which is either a natural passive limit cycle on a specific slope or a stable periodic walking gait on level ground generated with active control. Necessary and sufficient conditions are investigated for the existence and stability properties of periodic orbits on different slopes with the proposed control law. The adaptability and agility of undcractuated bipedal locomotion are greatly increased.
Fourthly, stable running problem of a planar underactuated biped robot which has two springy telescopic legs and one actuated joint in the hip is investigated. Based on a natural passive running limit cycle in level ground, a feedback control is proposed to stabilize the passive limit cycle and enlarge the basin of attraction. By this controller, there is no energy consumed when state vector of the robot reaches the running limit cycle under ideal impact condition. This conclusion is a great inspiration for achieving efficient human-like bipedal locomotion.
This dissertation gives rigorous theoretical proof for the proposed analysis and control design methods. Several simulations are given in each chapter to illustrate the results.
首先,针对基于被动的全驱动双足机器人,本文提出结合时间放缩和能量塑造的方法设计对应不同步长和步速的参考轨迹和过渡轨迹,采用反馈线性化的方法设计控制来扩大系统的收敛域,给出了每一步开始时刻更新的控制器条件,使步态响应轨迹和参考轨迹之间的误差渐近地收敛到零。首次从理论上解决了基于被动的全驱动双足机器人变步幅、变步速以及适应复杂环境的稳定行走控制问题,极大地提高了运动的灵活性。
其次,针对考虑欠驱动自由度的双足机器人的平衡站立控制问题,本文利用虚拟完整性约束方法,把机器人驱动关节的角度指定为支撑脚脚板与地面夹角的函数,给出了单脚稳定平衡站立所能承受的外界扰动范围的理论分析方法。当扰动较大,无法实现单脚平衡时,虚拟完整性约束会保证机器人变成双脚支撑状态以避免翻倒,这种扰动下的平衡动作和人非常类似。另外,针对一种特殊的欠驱动平衡站立问题—机器人单脚脚尖平衡站立,本文也首次从理论上给出了虚拟完整性约束设计条件和收敛域估计方法。
再次,针对更一般的欠驱动自由度为一的n自由度的双足机器人,本文首次提出结合时间放缩控制和受控对称性方法来设计统一的反馈控制器,成功实现了欠驱动机器人从一个原始的步态(这个原始的步态既可以是特定斜坡上的一个被动的极限环,也可以是主动控制作用下机器人在地面上产生的一个周期性的行走步态)产生不同斜坡上的周期性步态,并给出了不同斜坡上周期性步态存在性和稳定性的充分必要条件,应用该方法可以极大提高欠驱动双足运动的灵活性和适应性。
最后,本文研究了一种带有储能机构的欠驱动双足机器人的稳定奔跑问题,以其平地上存在的自然的被动奔跑极限环为基础,给出了反馈控制器设计方法,实现水平地面上稳定、节能的奔跑运动。基于文中的控制策略,在理想状态下,奔跑的步态收敛到被动的极限环上之后,系统将没有能量消耗,这一结论对于实现双足机器人高效的类人运动具有重要启示。
针对提出的控制器设计方法,本文在相应的各个章节给出了详细的理论分析,并通过数字仿真进行验证。
Bipedal humanoid robot has a great advantage in adaptability to the environment and strong affinity in human-machine interaction. However, there is a great disparity between bipedal locomotion developed by the existing control theory and real human bipedal loco-motion. Inspired by the passivity and underactuation existing in human bipedal locomotion, this dissertation combines passivity-based control, energy shaping control, hybrid zero dy-namics and time scaling control in order to study stable, agile and efficient locomotion control methods of bipedal robots based on passivity and underactuation. The contribution of this paper can be listed as follows:
Firstly, method combined time scaling control and energy shaping control is proposed for full actuated bipedal robot to construct reference trajectories with different step length and walking speed. A feedback control law is obtained via feedback linearization technique so that the trajectory of the robot converges to a desired passive walking gait. A larger basin of attraction can be obtained. Corresponding feedback control laws are updated at the beginning of each step. Then, the controller condition that the errors measuring the difference of the response trajectory and the reference one asymptotically converge to zero is given. The problem of achieving a stable walking in complex environments for full actuated bipedal robot with regulable step length and walking speed is first solved in this dissertation. The agility of bipedal locomotion is increased.
Secondly, balance control problem of planar bipedal robots with underactuation dur-ing disturbed standing is investigated. Virtual holonomic constraints which specify the an-gles of actuated joints as a function of the rotation angle between the sole of stance foot and ground are introduced. Several conditions guaranteeing the balance of standing for given virtual holonomic constraints arc obtained. Moreover, for a disturbance beyond the bal-ance conditions for single-leg support, robot changes to a double support posture to avoid turnover by the virtual holonomic constraints and this reaction is very human-like. Further, for a special kind of balance:standing on toe which leads to underactuation, the design conditions of virtual holonomic constraints and estimate set of basin of attraction are first given in theory.
Thirdly, a unified feedback control law for n degree-of-freedom biped robots with one degree of underactuation so as to generate periodic orbits on different slopes is first developed in this dissertation. The periodic orbits on different slopes are produced from an original periodic orbit, which is either a natural passive limit cycle on a specific slope or a stable periodic walking gait on level ground generated with active control. Necessary and sufficient conditions are investigated for the existence and stability properties of periodic orbits on different slopes with the proposed control law. The adaptability and agility of undcractuated bipedal locomotion are greatly increased.
Fourthly, stable running problem of a planar underactuated biped robot which has two springy telescopic legs and one actuated joint in the hip is investigated. Based on a natural passive running limit cycle in level ground, a feedback control is proposed to stabilize the passive limit cycle and enlarge the basin of attraction. By this controller, there is no energy consumed when state vector of the robot reaches the running limit cycle under ideal impact condition. This conclusion is a great inspiration for achieving efficient human-like bipedal locomotion.
This dissertation gives rigorous theoretical proof for the proposed analysis and control design methods. Several simulations are given in each chapter to illustrate the results.
引文
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