面向室内环境的人形机器人的运动控制
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摘要
人形机器人以其类人的外形逐渐从机器人中脱颖而出,为越来越多的学者所关注。目前对人形机器人的研究尚停留在室内环境。相对恶劣的自然环境室内环境虽然更加友好,但是人形机器人与身俱来的非线性、高维性以及不稳定性使双足运动控制成为近年来机器人技术领域的一个重要挑战。本文在回顾人形机器人的发展历程之后将详细从“稳定性判据”、“步行模式生成”和“反馈控制”三个方面详细介绍双足运动控制的研究现状。
机动性一词源于机器人世界杯RoboCup,具备较高机动性的机器人往往具有较高的控球率,从而能够获得比赛的主动权。对人形机器人来说机动性是很重要的,特别是在未来的家庭服务中,机器人需要及时的响应上层控制命令；需要具备遇到障碍物时及时躲避的能力；还需要具备较高的步行速度,以在最短时间内完成任务。本文将介绍一种高机动性的步行模式生成方法,该方法打破传统的常量ZMP模型,用两个三次样条曲线表示机器人一步中前向平面和侧向平面的ZMP轨迹,并同步规划生成每个控制周期的ZMP轨迹和质心轨迹。该方法响应上层控制命令的最大延迟为一个步行周期,最小延迟为一个控制周期,并能够在行走过程中一步实现任意的足迹切换。该方法还避免了双足支撑阶段ZMP轨迹的连接问题,从而使得速度进行平滑的过度,这对机器人频率的提升起到了至关重要的作用。此外,对于ZMP轨迹走向的不可控问题,我们给出了两个方法来进行优化和修正,分别是在线的以最短双足支撑时间为目标的优化方法和基于离散化技术对超出支撑多边形的ZMP轨迹的修正方法。
本文还将介绍一种全新的物理模型,该模型能够表示机器人躯干的角动量,对于进一步提高机器人的机动性具有重要作用。对此模型的动力学推导和基于离散化的数值解法本文也将详细给出。
近年来,一些高端机器人在国际上独领风骚,它们能够进行多种灵活的双足动作,如跑步、上下楼梯、在未建模的不平地面上行走等。当然,这些动作的实现很大程度上得益于它们高档的硬件和精密的做工,这也是使这些机器人的成本居高不下的原因。08年,NAO机器人成为RoboCup标准平台项目的标准比赛用机器人,其以完整的传感器系统和相对低廉的价格获得了大家的支持。低端机器人的兴起加速了人形机器人民用化和进入家庭的进程,对它们的研究具有重大的意义。低端机器人面临着一些问题,如弹性关节会导致电机控制的偏差,低精度和高延迟传感器会导致反馈控制的失败等。本文将以机器人NAO为平台,对其展开一系列的研究。
首先本文将介绍一种理论上的弹性关节前馈补偿方法,该方法基于拉格朗日方程,利用倒立摆模型求得机器人的关节补偿公式。我们还将使用机器人行走的特性来加速此补偿公式的计算,使其具备在线计算的能力。
本文还将介绍不同行走环境下的不同反馈控制策略组合。当机器人在平地行走时,我们采用基于惯性传感器的闭环步行模式生成方法和踝关节反馈控制两种策略,机器人能够以步行周期0.18[s]的高频运动进行稳定行走。当机器人在不平地面行走时,我们采用基于关节传感器的闭环步行模式生成方法和基于惯性传感器的姿态控制这两种反馈策略,还有两个反馈策略只在机器人遇到较大干扰时才会触发,它们是基于压力传感器的地面反作用力控制和机器人质心高度控制策略。该反馈策略的组合能够使得机器人在未建模的不平地面上进行稳定的双足行走,不平地面包括各种障碍物和不稳定的动态斜坡。
本文的主要贡献有四点：
第一,提出了一种满足机动性指标的步行模式生成方法,该方法根据最新的上层控制指令生成每步足迹,其响应高层控制命令的最大延迟仅为一个步行周期,最小延迟为一个控制周期,满足了及时响应控制指令的指标；该方法能够在行走过程中一步实现任意的足迹切换,不需要任何的预观时间,满足了实时迅速改变足迹的指标；本文在实体机器人Nao上实现了步行周期为0.18[s]的高频行走,带来速度质的提高,响应控制命令的最大延迟仅为0.18[s],最大前进速度达0.33[m/s],满足了最短时间到达目标点的机动性指标。
第二,惯有的对弹性关节的前馈补偿方法是经验式的,本文提出了基于拉格朗日方程的理论方法并使用倒立摆模型对其进行在线的计算,同时该方法利用多种技术对其进行了优化,从而实现了在线计算。此外,该方法还引申出一种计算关节弹性系数的方法。
第三,为NAO机器人设计了两套反馈策略组合,分别应用于平地和不平地面的行走。在平地上机器人能够稳定的进行高频行走；在不平地面上,机器人能够在充满障碍物的地面和不稳定斜坡上行走,实现了高端机器人才有的在未建模的不平地面上的行走能力。
第四,提出了一种全新的物理模型,利用角动量定理和达朗贝尔原则对该模型进行了详细的推导,同时给出该模型动力学公式的数值解法并对其进行了详细的误差分析。该模型可以生成包含躯干运动的双足行走,进一步提高了机器人的机动性。
More and more researchers paid attention to humanoid robots due to its outstand-ing humanoid shape. Currently, humanid robots are limited in indoor environment. Although this kind of environment is better than out-door conditions, biped locomo-tion control is still a challenge problem due to its intrinsic non-linaear property, high-dimension property, and instability. In this dissertation, after introducing the history of humanoid robots, a detailed research status will be given in terms of "Stability Crite-rion","Gait Pattern Generation", and "Feedback Control".
The word "Flexibility" comes from RoboCup. Robots that have flexible locomo-tion always have higher ball controlling percentage. In the future, humanoid robots will provide services to human beings and flexibility will be an important property in various application scenarios. First of all humanoid robots are required to respond to high level commands as soon as possible. Secondly, they need the ability of avoiding obstacles in a fast manner. Last but not the least, higher speed must be achieved to finish the task in shorter time. In this dissertation, a method of generating flexible gait pattern will be given. This method will not treat the ZMP of one step as constant point but use two cubic splines for sagittal direction and lateral direction. ZMP trajectories and CoG tra-jectories of every control cycle will be simultaneously planned. The maximum delay of responding to high level command is one step duration, while the minimum one is one control cycle. This method enables the robot change to arbitrary footstep in one step while playing dynamic walking. The traditional problem of connecting discrete ZMPs in double support phase is naturally avoided which plays an important role in increas-ing walking frequency. Besides, for the problem of uncontrollable ZMP trajectories, an optimization method and a refine method are given. The optimization method takes the goal of minimizing double support phase, so that the robot will have more time in single support phase. The refine method is performed in the case that the ZMP trajectories are out of the support polygon.
A new physical model will be introduced in this dissertation. This model can repre-sent the angular momentum of the trunk of the robot which is important for increasing flexibility once more. The detailed deduction of its dynamics will be given and the discrete numerical solution of the resulting dynamics will be discussed too.
Recently, some high-level robots are developed and showed fancy locomotion such as running, climing stairs, walking on uneven terrain that is not modeled in advance. And of course, this fancy locomotion gained profit from its high level hardware which makes those robots really expensive. In the year2008, robot NAO become the standard robot of standard platform league of RoboCup. NAO has a lot of sensors and a much cheaper price, so that it is accepted in many laboratories. This kind of low-level robots are conquering the world showing that humanoid robots will no longer be facilities of laboratory but furnitures of family. However, they suffer from low level sensors and elastic joints which lead to motor deflections. This dissertation will do massive researches on NAO.
First of all, the method of feed-forward compensation for elastic joint is given. It is based on Lagrange principle and obtains the compensation equations via inverted pendulum model. Besides, some optimization techniques are introduced to accelerate the computation and make it be able to be computed in real time.
Strategies integrated for different application scenarios are discussed in this disser-tation. When walking on planar surface, two strategies are used. They are closed-loop gait pattern generator based on inertial sensors and ankle feedback technique. When walking on uneven terrain, four strategies are integrated. Two of them are closed-loop gait pattern generator based on joint sensors and posture feedback control based on in-ertial sensors. The rest two strategies, i.e. ground reaction force control and CoG height control are used in emergency situation. This method enables the robot to walk on un-even terrain which is not modeled in advance. The uneven terrain consists of obstacles and a free-move slope.
The main contributions of this dissertation are showed as follows.
1. A method that satisfies flexibility benchmarks is given. Footstep is generated according to the latest high level command. The maximum delay of responding is one step duration, while the minimum delay is one control cycle. This satisfies the first benchmark which is "Responding to high level command in time". The robot is able to change to arbitrary footstep using just one step without any preview time. This sat-isfies the second benchmark which is "Change footstep in real time". This dissertation implemented a fast walking of which step duration is just0.18[s]. The delay of respond-ing is just0.18[s]. The maximum forward speed is0.33[m/s]. This satisfies the third benchmark which is "Reach target point as soon as possible"
2. A compensation method completely based on theory is discussed while the tra-ditional compensation is performed in an empirical way. It is based on the theory of Lagrange function. Linear inverted pendulum is also used to compute the compensa- tion. Several techniques are used to optimize the computation time resulting a real time method. Moreover, a technique of computing elastic coefficient is derived.
3. Feedback strategies are integrated deliberately for planar surface and uneven terrain. When walking on planar surface, the robot is able to perform stable high fre-quency walking. When walking on uneven terrain, the robot is able to walk on various obstacles and a movable slope. This work enables the robot to perform fancy locomo-tion just like the high level robots.
4. A new physics model is presented. The detailed deduction of its dynamics based on angular momentum theorem and D'Alembert principle is given. Moreover, a numer-ical solution of its dynamic equation is provided and its truncation error is discussed in detail. This model can represent angular momentum of the trunk of the robot which further enhances the flexibility of biped walking.
机动性一词源于机器人世界杯RoboCup,具备较高机动性的机器人往往具有较高的控球率,从而能够获得比赛的主动权。对人形机器人来说机动性是很重要的,特别是在未来的家庭服务中,机器人需要及时的响应上层控制命令；需要具备遇到障碍物时及时躲避的能力；还需要具备较高的步行速度,以在最短时间内完成任务。本文将介绍一种高机动性的步行模式生成方法,该方法打破传统的常量ZMP模型,用两个三次样条曲线表示机器人一步中前向平面和侧向平面的ZMP轨迹,并同步规划生成每个控制周期的ZMP轨迹和质心轨迹。该方法响应上层控制命令的最大延迟为一个步行周期,最小延迟为一个控制周期,并能够在行走过程中一步实现任意的足迹切换。该方法还避免了双足支撑阶段ZMP轨迹的连接问题,从而使得速度进行平滑的过度,这对机器人频率的提升起到了至关重要的作用。此外,对于ZMP轨迹走向的不可控问题,我们给出了两个方法来进行优化和修正,分别是在线的以最短双足支撑时间为目标的优化方法和基于离散化技术对超出支撑多边形的ZMP轨迹的修正方法。
本文还将介绍一种全新的物理模型,该模型能够表示机器人躯干的角动量,对于进一步提高机器人的机动性具有重要作用。对此模型的动力学推导和基于离散化的数值解法本文也将详细给出。
近年来,一些高端机器人在国际上独领风骚,它们能够进行多种灵活的双足动作,如跑步、上下楼梯、在未建模的不平地面上行走等。当然,这些动作的实现很大程度上得益于它们高档的硬件和精密的做工,这也是使这些机器人的成本居高不下的原因。08年,NAO机器人成为RoboCup标准平台项目的标准比赛用机器人,其以完整的传感器系统和相对低廉的价格获得了大家的支持。低端机器人的兴起加速了人形机器人民用化和进入家庭的进程,对它们的研究具有重大的意义。低端机器人面临着一些问题,如弹性关节会导致电机控制的偏差,低精度和高延迟传感器会导致反馈控制的失败等。本文将以机器人NAO为平台,对其展开一系列的研究。
首先本文将介绍一种理论上的弹性关节前馈补偿方法,该方法基于拉格朗日方程,利用倒立摆模型求得机器人的关节补偿公式。我们还将使用机器人行走的特性来加速此补偿公式的计算,使其具备在线计算的能力。
本文还将介绍不同行走环境下的不同反馈控制策略组合。当机器人在平地行走时,我们采用基于惯性传感器的闭环步行模式生成方法和踝关节反馈控制两种策略,机器人能够以步行周期0.18[s]的高频运动进行稳定行走。当机器人在不平地面行走时,我们采用基于关节传感器的闭环步行模式生成方法和基于惯性传感器的姿态控制这两种反馈策略,还有两个反馈策略只在机器人遇到较大干扰时才会触发,它们是基于压力传感器的地面反作用力控制和机器人质心高度控制策略。该反馈策略的组合能够使得机器人在未建模的不平地面上进行稳定的双足行走,不平地面包括各种障碍物和不稳定的动态斜坡。
本文的主要贡献有四点：
第一,提出了一种满足机动性指标的步行模式生成方法,该方法根据最新的上层控制指令生成每步足迹,其响应高层控制命令的最大延迟仅为一个步行周期,最小延迟为一个控制周期,满足了及时响应控制指令的指标；该方法能够在行走过程中一步实现任意的足迹切换,不需要任何的预观时间,满足了实时迅速改变足迹的指标；本文在实体机器人Nao上实现了步行周期为0.18[s]的高频行走,带来速度质的提高,响应控制命令的最大延迟仅为0.18[s],最大前进速度达0.33[m/s],满足了最短时间到达目标点的机动性指标。
第二,惯有的对弹性关节的前馈补偿方法是经验式的,本文提出了基于拉格朗日方程的理论方法并使用倒立摆模型对其进行在线的计算,同时该方法利用多种技术对其进行了优化,从而实现了在线计算。此外,该方法还引申出一种计算关节弹性系数的方法。
第三,为NAO机器人设计了两套反馈策略组合,分别应用于平地和不平地面的行走。在平地上机器人能够稳定的进行高频行走；在不平地面上,机器人能够在充满障碍物的地面和不稳定斜坡上行走,实现了高端机器人才有的在未建模的不平地面上的行走能力。
第四,提出了一种全新的物理模型,利用角动量定理和达朗贝尔原则对该模型进行了详细的推导,同时给出该模型动力学公式的数值解法并对其进行了详细的误差分析。该模型可以生成包含躯干运动的双足行走,进一步提高了机器人的机动性。
More and more researchers paid attention to humanoid robots due to its outstand-ing humanoid shape. Currently, humanid robots are limited in indoor environment. Although this kind of environment is better than out-door conditions, biped locomo-tion control is still a challenge problem due to its intrinsic non-linaear property, high-dimension property, and instability. In this dissertation, after introducing the history of humanoid robots, a detailed research status will be given in terms of "Stability Crite-rion","Gait Pattern Generation", and "Feedback Control".
The word "Flexibility" comes from RoboCup. Robots that have flexible locomo-tion always have higher ball controlling percentage. In the future, humanoid robots will provide services to human beings and flexibility will be an important property in various application scenarios. First of all humanoid robots are required to respond to high level commands as soon as possible. Secondly, they need the ability of avoiding obstacles in a fast manner. Last but not the least, higher speed must be achieved to finish the task in shorter time. In this dissertation, a method of generating flexible gait pattern will be given. This method will not treat the ZMP of one step as constant point but use two cubic splines for sagittal direction and lateral direction. ZMP trajectories and CoG tra-jectories of every control cycle will be simultaneously planned. The maximum delay of responding to high level command is one step duration, while the minimum one is one control cycle. This method enables the robot change to arbitrary footstep in one step while playing dynamic walking. The traditional problem of connecting discrete ZMPs in double support phase is naturally avoided which plays an important role in increas-ing walking frequency. Besides, for the problem of uncontrollable ZMP trajectories, an optimization method and a refine method are given. The optimization method takes the goal of minimizing double support phase, so that the robot will have more time in single support phase. The refine method is performed in the case that the ZMP trajectories are out of the support polygon.
A new physical model will be introduced in this dissertation. This model can repre-sent the angular momentum of the trunk of the robot which is important for increasing flexibility once more. The detailed deduction of its dynamics will be given and the discrete numerical solution of the resulting dynamics will be discussed too.
Recently, some high-level robots are developed and showed fancy locomotion such as running, climing stairs, walking on uneven terrain that is not modeled in advance. And of course, this fancy locomotion gained profit from its high level hardware which makes those robots really expensive. In the year2008, robot NAO become the standard robot of standard platform league of RoboCup. NAO has a lot of sensors and a much cheaper price, so that it is accepted in many laboratories. This kind of low-level robots are conquering the world showing that humanoid robots will no longer be facilities of laboratory but furnitures of family. However, they suffer from low level sensors and elastic joints which lead to motor deflections. This dissertation will do massive researches on NAO.
First of all, the method of feed-forward compensation for elastic joint is given. It is based on Lagrange principle and obtains the compensation equations via inverted pendulum model. Besides, some optimization techniques are introduced to accelerate the computation and make it be able to be computed in real time.
Strategies integrated for different application scenarios are discussed in this disser-tation. When walking on planar surface, two strategies are used. They are closed-loop gait pattern generator based on inertial sensors and ankle feedback technique. When walking on uneven terrain, four strategies are integrated. Two of them are closed-loop gait pattern generator based on joint sensors and posture feedback control based on in-ertial sensors. The rest two strategies, i.e. ground reaction force control and CoG height control are used in emergency situation. This method enables the robot to walk on un-even terrain which is not modeled in advance. The uneven terrain consists of obstacles and a free-move slope.
The main contributions of this dissertation are showed as follows.
1. A method that satisfies flexibility benchmarks is given. Footstep is generated according to the latest high level command. The maximum delay of responding is one step duration, while the minimum delay is one control cycle. This satisfies the first benchmark which is "Responding to high level command in time". The robot is able to change to arbitrary footstep using just one step without any preview time. This sat-isfies the second benchmark which is "Change footstep in real time". This dissertation implemented a fast walking of which step duration is just0.18[s]. The delay of respond-ing is just0.18[s]. The maximum forward speed is0.33[m/s]. This satisfies the third benchmark which is "Reach target point as soon as possible"
2. A compensation method completely based on theory is discussed while the tra-ditional compensation is performed in an empirical way. It is based on the theory of Lagrange function. Linear inverted pendulum is also used to compute the compensa- tion. Several techniques are used to optimize the computation time resulting a real time method. Moreover, a technique of computing elastic coefficient is derived.
3. Feedback strategies are integrated deliberately for planar surface and uneven terrain. When walking on planar surface, the robot is able to perform stable high fre-quency walking. When walking on uneven terrain, the robot is able to walk on various obstacles and a movable slope. This work enables the robot to perform fancy locomo-tion just like the high level robots.
4. A new physics model is presented. The detailed deduction of its dynamics based on angular momentum theorem and D'Alembert principle is given. Moreover, a numer-ical solution of its dynamic equation is provided and its truncation error is discussed in detail. This model can represent angular momentum of the trunk of the robot which further enhances the flexibility of biped walking.
引文
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