六足仿生机器人的研制及其运动规划研究
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摘要
随着人类探索自然界步伐的不断加速,各应用领域对具有复杂环境自主移动能力机器人的需求,日趋广泛而深入。理论上,足式机器人具有比轮式机器人更加卓越的应对复杂地形的能力,因而被给予了巨大的关注,但到目前为止,由于自适应步行控制算法匮乏等原因,足式移动方式在许多实际应用中还无法付诸实践。另一方面,作为地球上最成功的运动生物,多足昆虫则以其复杂精妙的肢体结构和简易灵巧的运动控制策略,轻易地穿越了各种复杂的自然地形,甚至能在光滑的表面上倒立行走。因此,将多足昆虫的行为学研究成果,融入到步行机器人的设计与控制中,开发具有卓越移动能力的六足仿生机器人,对于足式移动机器人技术的研究与应用具有重要的理论和现实意义。
本文从仿生的角度出发,对六足步行机器人的构形设计、理论建模、运动规划、控制系统设计等方面进行了深入探讨,并通过实验对其在复杂环境中的应用进行了研究。
系统设计方面,将多足昆虫的步行结构建模为具有三自由度腿及椭圆状肢体分布的构形;设计了舵机驱动、平行四连杆传动的具有全方位移动能力的本体结构;以腿部肢节比例、基节轴线方向为自变量,参考位姿下机器人躯干的六维运动尺度为因变量,构造灵活度目标函数对结构参数进行了优化。设计了由上位机PC、嵌入式主控制器、信号采集与驱动控制器组成的层次化控制系统硬件结构,实现了由步态控制、肢体控制、关节电机、传感感知、通信模块组成的模块化控制系统软件架构。对步行控制任务进行功能和行为组合分解,提出了基于功能行为集成的分布式步态控制结构和自由步态步行控制模式与腿部反射控制模式相结合的复杂地形步行总体控制模式。
运动学与动力学分析方面,在多足昆虫结构建模基础上,建立了六足仿生机器人的运动学模型,综合运用串、并联机构学理论,分别推导了单足摆动腿和多足支撑腿的位置、速度、加速度运动学方程。基于达朗伯原理建立六足机器人的拉格朗日动力学模型,运用运动影响系数机构学理论将系统受到的所有力都折算到广义坐标上来建立力平衡方程进行动力学求解,推导出拉格朗日动力学方程;探讨了驱动力矩超确定输入问题,依据能量守恒原理和运动影响系数理论,推导了所有输入力矩的协调方程。通过仿真实验进行了运动学正确性验证及机器人动力学特性的仿真测试。
腿部轨迹规划方面,分别针对地形平坦或轻度崎岖以及重度崎岖的情形,提出了轻度崎岖地形轨迹规划策略和重度崎岖地形腿部反射轨迹规划策略。对于前者,构建了统一的摆动相和支撑相轨迹规划描述,提出了基于缓冲区的摆动相组合多项式曲线轨迹规划策略,并依据相对运动原理将支撑相规划的并联闭链问题转化为串联开链问题。对于后者,采用具有圆弧过渡的组合直线足端轨迹建立了抬腿和寻落反射机制的人工实现模型;并根据步行需要提出了单次反射、多次反射、复合反射的人工反射模式。
步态规划方面,通过多足昆虫步态分析和抽象,推导出步行速度与步态模式间的数学关联,提出了多足步行的调速方法;提出了基于相位时钟的腿间相序描述方法和基于腿间相序调整的自由步态形成原理。综合考虑加速度因素的影响,提出一种基于改进能量稳定裕度法的稳定性判定方法,推导了六足步行稳定裕度与步长及步行加速度的数学关联,并给出了维持静态稳定步行的步态参数域。依据自由步态形成原理,提出了腿间相序的调整策略和作用于相邻腿之间的局部规则,借助分布式局部规则网络,分别应用基于有限状态机的狭义步态控制算法与广义步态控制算法,实时地自适应调整错乱的腿间相序,生成了静态稳定的自由步态,通过仿真实验进行了验证。
在设计搭建的六足仿生机器人步行实验平台上,分别实施了固化步态步行实验、腿部反射步行实验、自由步态步行实验,不仅验证了所提出的六足步行理论的正确性,同时也例证了机器人的复杂地形自适应稳定步行能力。
With the increasingly rapid step of human exploration of nature, the demand for robots with autonomous mobility under complex environment has been getting broader and deeper in more and more application areas. Theoretically, legged robot offers more superior performance of dealing with complicated terrain conditions than that provided by wheeled robot and therefore has been given great concern, however up to now, for the reason of absence of adaptive walk control algorithm, legged locomotion means still could not be put into practice in many practical applications yet. While on the other hand, as the most successful moving creature on the earth, multi-legged insect has facilely managed to surmount various complex natural landforms and even to walk upside down on smooth surfaces by right of its sophisticated limb structure and dexterous locomotion control strategies. Accordingly, it contains great theoretical and practical significance for the research and application of legged mobile robotics to blend the behavioral research effort of multi-legged insect into the design and control of walking robot and furthermore to develop hexapod biomimetic robots with more superexcellent mobility.
In this work, a thorough investigation of configuration design, theoretical modeling, motion planning and contriving of control system were made in terms of bionics, and moreover, an intensive experimental study on its application in complex environment was performed simultaneously.
From the aspect of robot system design, the walking structure of multi-legged insect was modeled as a configuration with 3-DOF legs and ellipse distribution of limbs; a mechanical configuration capable of omni-directional locomotion was fabricated with rudder-driven and parallel four-bar linkage transmission; by taking segment proportion and orientation of coax axes as the independent variables, and locomotion ranges of the robot body in six dimensions under reference posture as the attributive variables, an objective estimation function of mobility was constructed and the structure parameters were optimized. Stratified hardware structure comprised of upper PC, embedded main controller, controller of signal acquisition, drive unit and modularized software structure comprised of gait control, limb control, joint motor, sensing unit, communication module of the control system were developed. The task of walking control was functionally and behaviorally decomposed combinedly, further, a distributed gait control structure based on function-behavior-integration and an overall walking control mode combined with control mode of free gait and that of leg-end reflex applied under complicated terrain conditions were presented.
From the aspect of kinematics and dynamics analysis, the kinematic model of hexapod biomimetic robot was established on the basis of structural modeling of multi-legged insect, besides, kinematic equations of position, velocity and acceleration of single swinging leg and multiple supporting legs were deduced separately by means of theories of serial and parallel mechanics. The Lagrange dynamic model of the hexapod robot was established based on the alembert principle, and by converting the entire forces endured by the robot system onto the generalized coordinates by means of the influence coefficient method of theory of mechanics, the equilibrium equations were established, the dynamics calculation was performed and further the Lagrange dynamic equations were deduced; the issue of over-determined torque input was discussed, and the cooperating equations of entire inputted torques were deduced in the light of the law of conservation of energy and the influence coefficient method of theory of mechanics. Through the simulation experiments, validity of kinematics was testified and the simulation testing of the dynamics characters of the robot system was performed.
From the aspect of trajectory planning, a trajectory planning strategy of free gait and that of leg-end reflex were put forward aiming at separately the situations of slightly irregular and badly irregular terrain conditions. For the former one, a uniform trajectory planning description of stance phase and swing phase was upbuilt, a buffer-area-based trajectory planning strategy of swing phase using combined polynomial curve was proposed, and the problem of parallel closed link was transformed into the one of serial open link according to the principle of relative locomotion. While as to the latter one, the artificial realization modes of elevator reflex and searching reflex mechanisms were established by adopting the leg-end trajectory of combined beelines with camber transition; and according to the demand of walking, the artificial reflex modes of single reflex, multiple reflex and combined reflex were put forward.
From the aspect of gait planning, by means of analysis and abstraction of multi-legged insect gait, the mathematical relationship of walking velocity and gait pattern was deduced and the velocity modulation method of multi-legged walking was presented; moreover, a phase-clock-based description of inter-leg phase sequence was proposed, and a principle of free gait generation was presented based on the adjustment of inter-leg phase sequence. By ways of comprehensively considering the effect of acceleration factor, a stability determination method based on the Improved Energy Stability Margin was put forward, the mathematical relationship of stability margin and step length, walking acceleration of hexapod walking was deduced, and the region of gait parameters by which the statically stable walking was maintained was presented. According to the principle of free gait generation, a regulation strategy of inter-leg phase sequence and a set of local rules operating between adjacent legs were put forward, further, by means of a distributed network of local rules and based on the theory of Finite State Machine, a specialized and a generalized control algorithms of free gait generation were applied separately to adaptively regulate the fluctuation of inter-leg phase sequence and therefore generate statically stable free gait, besides, the algorithms were testified by the simulation experiments.
With the walking experimental platform of hexapod biomimetic robot, walking experiments of fixed gait, leg-end reflex and free gait were executed separately, which not only testified the validity of the hexapod walking theories proposed but also exemplified the adaptive stable locomotion ability of the robot under complex terrain conditions.
本文从仿生的角度出发,对六足步行机器人的构形设计、理论建模、运动规划、控制系统设计等方面进行了深入探讨,并通过实验对其在复杂环境中的应用进行了研究。
系统设计方面,将多足昆虫的步行结构建模为具有三自由度腿及椭圆状肢体分布的构形;设计了舵机驱动、平行四连杆传动的具有全方位移动能力的本体结构;以腿部肢节比例、基节轴线方向为自变量,参考位姿下机器人躯干的六维运动尺度为因变量,构造灵活度目标函数对结构参数进行了优化。设计了由上位机PC、嵌入式主控制器、信号采集与驱动控制器组成的层次化控制系统硬件结构,实现了由步态控制、肢体控制、关节电机、传感感知、通信模块组成的模块化控制系统软件架构。对步行控制任务进行功能和行为组合分解,提出了基于功能行为集成的分布式步态控制结构和自由步态步行控制模式与腿部反射控制模式相结合的复杂地形步行总体控制模式。
运动学与动力学分析方面,在多足昆虫结构建模基础上,建立了六足仿生机器人的运动学模型,综合运用串、并联机构学理论,分别推导了单足摆动腿和多足支撑腿的位置、速度、加速度运动学方程。基于达朗伯原理建立六足机器人的拉格朗日动力学模型,运用运动影响系数机构学理论将系统受到的所有力都折算到广义坐标上来建立力平衡方程进行动力学求解,推导出拉格朗日动力学方程;探讨了驱动力矩超确定输入问题,依据能量守恒原理和运动影响系数理论,推导了所有输入力矩的协调方程。通过仿真实验进行了运动学正确性验证及机器人动力学特性的仿真测试。
腿部轨迹规划方面,分别针对地形平坦或轻度崎岖以及重度崎岖的情形,提出了轻度崎岖地形轨迹规划策略和重度崎岖地形腿部反射轨迹规划策略。对于前者,构建了统一的摆动相和支撑相轨迹规划描述,提出了基于缓冲区的摆动相组合多项式曲线轨迹规划策略,并依据相对运动原理将支撑相规划的并联闭链问题转化为串联开链问题。对于后者,采用具有圆弧过渡的组合直线足端轨迹建立了抬腿和寻落反射机制的人工实现模型;并根据步行需要提出了单次反射、多次反射、复合反射的人工反射模式。
步态规划方面,通过多足昆虫步态分析和抽象,推导出步行速度与步态模式间的数学关联,提出了多足步行的调速方法;提出了基于相位时钟的腿间相序描述方法和基于腿间相序调整的自由步态形成原理。综合考虑加速度因素的影响,提出一种基于改进能量稳定裕度法的稳定性判定方法,推导了六足步行稳定裕度与步长及步行加速度的数学关联,并给出了维持静态稳定步行的步态参数域。依据自由步态形成原理,提出了腿间相序的调整策略和作用于相邻腿之间的局部规则,借助分布式局部规则网络,分别应用基于有限状态机的狭义步态控制算法与广义步态控制算法,实时地自适应调整错乱的腿间相序,生成了静态稳定的自由步态,通过仿真实验进行了验证。
在设计搭建的六足仿生机器人步行实验平台上,分别实施了固化步态步行实验、腿部反射步行实验、自由步态步行实验,不仅验证了所提出的六足步行理论的正确性,同时也例证了机器人的复杂地形自适应稳定步行能力。
With the increasingly rapid step of human exploration of nature, the demand for robots with autonomous mobility under complex environment has been getting broader and deeper in more and more application areas. Theoretically, legged robot offers more superior performance of dealing with complicated terrain conditions than that provided by wheeled robot and therefore has been given great concern, however up to now, for the reason of absence of adaptive walk control algorithm, legged locomotion means still could not be put into practice in many practical applications yet. While on the other hand, as the most successful moving creature on the earth, multi-legged insect has facilely managed to surmount various complex natural landforms and even to walk upside down on smooth surfaces by right of its sophisticated limb structure and dexterous locomotion control strategies. Accordingly, it contains great theoretical and practical significance for the research and application of legged mobile robotics to blend the behavioral research effort of multi-legged insect into the design and control of walking robot and furthermore to develop hexapod biomimetic robots with more superexcellent mobility.
In this work, a thorough investigation of configuration design, theoretical modeling, motion planning and contriving of control system were made in terms of bionics, and moreover, an intensive experimental study on its application in complex environment was performed simultaneously.
From the aspect of robot system design, the walking structure of multi-legged insect was modeled as a configuration with 3-DOF legs and ellipse distribution of limbs; a mechanical configuration capable of omni-directional locomotion was fabricated with rudder-driven and parallel four-bar linkage transmission; by taking segment proportion and orientation of coax axes as the independent variables, and locomotion ranges of the robot body in six dimensions under reference posture as the attributive variables, an objective estimation function of mobility was constructed and the structure parameters were optimized. Stratified hardware structure comprised of upper PC, embedded main controller, controller of signal acquisition, drive unit and modularized software structure comprised of gait control, limb control, joint motor, sensing unit, communication module of the control system were developed. The task of walking control was functionally and behaviorally decomposed combinedly, further, a distributed gait control structure based on function-behavior-integration and an overall walking control mode combined with control mode of free gait and that of leg-end reflex applied under complicated terrain conditions were presented.
From the aspect of kinematics and dynamics analysis, the kinematic model of hexapod biomimetic robot was established on the basis of structural modeling of multi-legged insect, besides, kinematic equations of position, velocity and acceleration of single swinging leg and multiple supporting legs were deduced separately by means of theories of serial and parallel mechanics. The Lagrange dynamic model of the hexapod robot was established based on the alembert principle, and by converting the entire forces endured by the robot system onto the generalized coordinates by means of the influence coefficient method of theory of mechanics, the equilibrium equations were established, the dynamics calculation was performed and further the Lagrange dynamic equations were deduced; the issue of over-determined torque input was discussed, and the cooperating equations of entire inputted torques were deduced in the light of the law of conservation of energy and the influence coefficient method of theory of mechanics. Through the simulation experiments, validity of kinematics was testified and the simulation testing of the dynamics characters of the robot system was performed.
From the aspect of trajectory planning, a trajectory planning strategy of free gait and that of leg-end reflex were put forward aiming at separately the situations of slightly irregular and badly irregular terrain conditions. For the former one, a uniform trajectory planning description of stance phase and swing phase was upbuilt, a buffer-area-based trajectory planning strategy of swing phase using combined polynomial curve was proposed, and the problem of parallel closed link was transformed into the one of serial open link according to the principle of relative locomotion. While as to the latter one, the artificial realization modes of elevator reflex and searching reflex mechanisms were established by adopting the leg-end trajectory of combined beelines with camber transition; and according to the demand of walking, the artificial reflex modes of single reflex, multiple reflex and combined reflex were put forward.
From the aspect of gait planning, by means of analysis and abstraction of multi-legged insect gait, the mathematical relationship of walking velocity and gait pattern was deduced and the velocity modulation method of multi-legged walking was presented; moreover, a phase-clock-based description of inter-leg phase sequence was proposed, and a principle of free gait generation was presented based on the adjustment of inter-leg phase sequence. By ways of comprehensively considering the effect of acceleration factor, a stability determination method based on the Improved Energy Stability Margin was put forward, the mathematical relationship of stability margin and step length, walking acceleration of hexapod walking was deduced, and the region of gait parameters by which the statically stable walking was maintained was presented. According to the principle of free gait generation, a regulation strategy of inter-leg phase sequence and a set of local rules operating between adjacent legs were put forward, further, by means of a distributed network of local rules and based on the theory of Finite State Machine, a specialized and a generalized control algorithms of free gait generation were applied separately to adaptively regulate the fluctuation of inter-leg phase sequence and therefore generate statically stable free gait, besides, the algorithms were testified by the simulation experiments.
With the walking experimental platform of hexapod biomimetic robot, walking experiments of fixed gait, leg-end reflex and free gait were executed separately, which not only testified the validity of the hexapod walking theories proposed but also exemplified the adaptive stable locomotion ability of the robot under complex terrain conditions.
引文
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36 R. Altendorfer, N. Moore, H. Komsuoglu. RHex: A Biologically Inspired Hexapod Runner. Autonomous Robots. 2001, 11: 207-213
37 E. Z. Moore. Reliable Stair Climbing in the Simple Hexapod RHex. The IEEE International Conference on Robotics and Automation, Washington DC, USA, 2002, 3: 2222-2227
38 D. Campbell, M. Buehler. Stair Descent in the Simple Hexapod RHex. The IEEE International Conference on Robotics and Automation, Taipei, Taiwan, 2003: 1380-1385
39 D. E. Koditschek, R. J. Full, M. Buehler. A Principled Approach to Bioinspired Design of Legged Locomotion Systems. The International Society for Optical Engineering, Bellingham, WA, 2004, 5422: 86-100
40 P. C. Lin, H. Komsuoglu, D. E. Koditschek. A Leg Configuration Measurement System for Full-Body Pose Estimates in a Hexapod Robot. IEEE Transactions on Robotics. 2005, 21(3): 411-422
41 B. Howley, M. Cutkosky. Safe Control of Hopping in Uneven Terrain. Journal of Dynamic Systems, Measurement and Control. 2009, 131(1): 1-11
42 S. Sponberg, R. J. Full. Neuromechanical Response of Musculo-skeletal Structures in Cockroaches During Rapid Running on Rough Terrain. The Journal of Experimental Biology. 2008, 211: 433-446
43 A. Saunders, D. I. Goldman, R. J. Full, M. Buehler. The RiSE climbing robot: Body and leg design. The International Society for Optical Engineering, Orlando, FL, 2006, 6230: 623017
44 M. J. Spenko, G. C. Haynes, J. A. Saunders, M. R. Cutkosky, A. A. Rizzi. Biologically Inspired Climbing with a Hexapedal Robot. Journal of Field Robotics. 2008, 25(4-5): 223-242
45 A. A. Rizzi, G. C. Haynes, R. J. Full, D. E. Koditschek. Gait Generation and Control in a Climbing Hexapod Robot. International Society for Optical Engineering, Orlando, FL, 2006, 6230(623018): 1-12
46刘凌云,郑光美.普通动物学.科学出版社, 2005: 221-257
47 D. Voth. Nature’s Guide to Robot Design. IEEE intelligent systems. 2002, 17:4-7
48蒋宗礼.人工神经网络导论.高等教育出版社, 2001: 1-14
49 D. Wettergreen, C. Thorpe. Developing Planning and Reactive Control for a Hexapod Robot. The IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, 1996: 2718-2723
50 E. Krotkov, R. Simmons. Perception, Planning, and Control for Autonomous Walking with the Ambler Planetary Rover. Journal of Robotics Research. 1996,
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51 B. Goodwine, J. W. Burdick. Motion Planning for Kinematic Stratified Systems with Application to Quasi-static Legged Locomotion and Finger Gaiting. IEEE Transactions on Robotics and Automation. 2002, 18(2): 209-222
52 F. Delcomyn. Neural Basis of Rhythmic Behavior in Animals. Science. 1980, 210: 492-498
53 H. Cruse, T. Kindermann, M. Schumm. Walknet - a Biologically Inspired Network to Control Six-legged Walking. Neural Networks. 1998, 11(7-8): 1435-1447
54 J. Schmitz, J. Dean, T. Kindermann. A Biologically Inspired Controller for Hexapod Walking: Simple Solutions by Exploiting Physical Properties. Biological Bulletin. 2001, 200: 195-200
55 V. Durr, J. Schmitz, H. Cruse. Behaviour-based Modelling of Hexapod Locomotion: Linking Biology and Technical Application. Arthropod Structure and Development. 2004, 33: 237-250
56 K. W. Wait, M. Goldfarb. A Biologically Inspired Approach to the Coordination of Hexapedal Gait. The IEEE International Conference on Robotics and Automation, Rome, Italy, 2007: 275-280
57 D. B. Randall, D. Q. Roger, J. C. Hillel, E. R. Roy. Biologically Inspired Approaches to Robotics. Communications of the ACM. 1997, 40(3): 31-38
58 M. Frik, A. Buschmann, M. Guddat, M. Karatas, D. C. Losch. AutonomousLocomotion of Walking Machines in Rough Terrain. The Thirteenth CISM-IFToMM Symposium, Zakopane, Poland, 2000: 331-338
59 T. Zielinska, J. Heng. Development of a Walking Machine: Mechanical Design and Control Problems. Mechatronics. 2002 (12): 737-754
60 R. A. Brooks. A Robust Layered Control System for a Mobile Robot. IEEE Journal of Robotics and Automation. 1986, RA-2(1): 14-23
61 E. Celaya, J. L. Albarral. Implementation of a Hierarchical Walk Controller for the LAURON III Hexapod Robot. The International Conference on Climbing and Walking Robots, Catania, Italy, 2003: 409-416
62 J. M. Porta, E. Celaya. Reactive Free-gait Generation to Follow Arbitrary Trajectories with a Hexapod Robot. Robotics and Autonomous Systems. 2004, 47(4): 187-201
63 E. Celaya, J. M. Porta. A Control Structure for the Locomotion of a Legged Robot on Difficult Terrain. IEEE Robotics and Automation Magazine. 1998, 5(2): 43-51.
64 E. Celaya, J. M. Porta. Control of a Six-legged Robot Walking on Abrupt Terrain. The IEEE International Conference on Robotics and Automation, Minneapolis, USA, 1996: 2731-2736
65 O. Janrathitikarn, L. N. Long. Gait Control of a Six-legged Robot on Unlevel Terrain Using a Cognitive Architecture. The IEEE Aerospace Conference, Big Sky, USA, 2008: 70-78
66顾冬雷,陈卫东,席裕庚.移动机器人条件反射能力的实现.机器人. 2001, 23(2): 123-126
67 M. S. Erden, K. Leblebiciolu. Multi Legged Walking in Robotics and Dynamic Gait Pattern Generation for a Six-legged Robot with Reinforcement Learning. In Mobile Robots: New Research. New York: Nova. 2005
68 J. M. Porta, E. Celaya. Efficient Gait Generation Using Reinforcement Learning. The International Conference on Climbing and Walking Robots, Karlsruhe, Germany, 2001: 411-418
69 M. S. Erden, K. Leblebicioglu. Free Gait Generation with Reinforcement Learning for a Six-legged Robot. Robotics and Autonomous Systems. 2008, 56(3): 199-212
70 J. Dean, G. Wendler. Stick Insect Locomotion on a Walking Wheel: Inter-leg Coordination of Leg Position. Journal of Experimental Biology. 1983, 103: 75-94
71 K. G. Pearson, R. Franklin. Characteristics of Leg Movements and Patterns of Coordination in Locusts Walking on Rough Terrain. Journal of Robotics Research. 1984, 3(2): 101-112
72 Bettina Blasing. Crossing Large Gaps: A Simulation Study of Stick Insect Behavior. Adaptive Behavior. 2006, 14(3): 265-285
73 H. Cruse. The Control of the Anterior Extreme Position of the Hind leg of a Walking Stick Insect, Carausius Morosus. Physiological Entomology. 1979, 4: 121-124
74 H. Cruse. What Mechanisms Coordinate Leg Movement in Walking Arthropods. Trends in Neuroscience. 1990, 13: 15-20
75 W. A. Lewinger, M. S. Branicky, R. D. Quinn. Insect-inspired, Actively Compliant Hexapod Capable of Object Manipulation. The International Conference on Climbing and Walking Robots, London, UK, 2005: 65-72
76 M. R. Fielding, G. R. Dunlop. Omnidirectional Hexapod Walking and Efficient Gaits Using Restrictedness. The International Journal of Robotics Research. 2004, 23(10-11): 1105-1110
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30 Kenji Inoue, Taisuke Tsurutani, Tomohito Takubo, Tatsuo Arai. Omni-directional Gait of Limb Mechanism Robot Hanging from Grid-like Structure. The IEEEInternational Conference on Intelligent Robots and Systems, Beijing, China, 2006: 1732-1737
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34 G. S. Dordevic, M. Rasic, R. Shadmehr. Parametric Models for Motion Planning and Control in Biomimetic Robotics. IEEE Transactions on Robotics. 2005, 21(1): 80-92
35 S. Kim, J. E. Clark, M. R. Cutkosky. ISprawl: Design and Tuning for High-speed Autonomous Open-loop Running. International Journal of Robotics Research. 2006, 25(9): 903-912
36 R. Altendorfer, N. Moore, H. Komsuoglu. RHex: A Biologically Inspired Hexapod Runner. Autonomous Robots. 2001, 11: 207-213
37 E. Z. Moore. Reliable Stair Climbing in the Simple Hexapod RHex. The IEEE International Conference on Robotics and Automation, Washington DC, USA, 2002, 3: 2222-2227
38 D. Campbell, M. Buehler. Stair Descent in the Simple Hexapod RHex. The IEEE International Conference on Robotics and Automation, Taipei, Taiwan, 2003: 1380-1385
39 D. E. Koditschek, R. J. Full, M. Buehler. A Principled Approach to Bioinspired Design of Legged Locomotion Systems. The International Society for Optical Engineering, Bellingham, WA, 2004, 5422: 86-100
40 P. C. Lin, H. Komsuoglu, D. E. Koditschek. A Leg Configuration Measurement System for Full-Body Pose Estimates in a Hexapod Robot. IEEE Transactions on Robotics. 2005, 21(3): 411-422
41 B. Howley, M. Cutkosky. Safe Control of Hopping in Uneven Terrain. Journal of Dynamic Systems, Measurement and Control. 2009, 131(1): 1-11
42 S. Sponberg, R. J. Full. Neuromechanical Response of Musculo-skeletal Structures in Cockroaches During Rapid Running on Rough Terrain. The Journal of Experimental Biology. 2008, 211: 433-446
43 A. Saunders, D. I. Goldman, R. J. Full, M. Buehler. The RiSE climbing robot: Body and leg design. The International Society for Optical Engineering, Orlando, FL, 2006, 6230: 623017
44 M. J. Spenko, G. C. Haynes, J. A. Saunders, M. R. Cutkosky, A. A. Rizzi. Biologically Inspired Climbing with a Hexapedal Robot. Journal of Field Robotics. 2008, 25(4-5): 223-242
45 A. A. Rizzi, G. C. Haynes, R. J. Full, D. E. Koditschek. Gait Generation and Control in a Climbing Hexapod Robot. International Society for Optical Engineering, Orlando, FL, 2006, 6230(623018): 1-12
46刘凌云,郑光美.普通动物学.科学出版社, 2005: 221-257
47 D. Voth. Nature’s Guide to Robot Design. IEEE intelligent systems. 2002, 17:4-7
48蒋宗礼.人工神经网络导论.高等教育出版社, 2001: 1-14
49 D. Wettergreen, C. Thorpe. Developing Planning and Reactive Control for a Hexapod Robot. The IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, 1996: 2718-2723
50 E. Krotkov, R. Simmons. Perception, Planning, and Control for Autonomous Walking with the Ambler Planetary Rover. Journal of Robotics Research. 1996,
15(2): 155-180
51 B. Goodwine, J. W. Burdick. Motion Planning for Kinematic Stratified Systems with Application to Quasi-static Legged Locomotion and Finger Gaiting. IEEE Transactions on Robotics and Automation. 2002, 18(2): 209-222
52 F. Delcomyn. Neural Basis of Rhythmic Behavior in Animals. Science. 1980, 210: 492-498
53 H. Cruse, T. Kindermann, M. Schumm. Walknet - a Biologically Inspired Network to Control Six-legged Walking. Neural Networks. 1998, 11(7-8): 1435-1447
54 J. Schmitz, J. Dean, T. Kindermann. A Biologically Inspired Controller for Hexapod Walking: Simple Solutions by Exploiting Physical Properties. Biological Bulletin. 2001, 200: 195-200
55 V. Durr, J. Schmitz, H. Cruse. Behaviour-based Modelling of Hexapod Locomotion: Linking Biology and Technical Application. Arthropod Structure and Development. 2004, 33: 237-250
56 K. W. Wait, M. Goldfarb. A Biologically Inspired Approach to the Coordination of Hexapedal Gait. The IEEE International Conference on Robotics and Automation, Rome, Italy, 2007: 275-280
57 D. B. Randall, D. Q. Roger, J. C. Hillel, E. R. Roy. Biologically Inspired Approaches to Robotics. Communications of the ACM. 1997, 40(3): 31-38
58 M. Frik, A. Buschmann, M. Guddat, M. Karatas, D. C. Losch. AutonomousLocomotion of Walking Machines in Rough Terrain. The Thirteenth CISM-IFToMM Symposium, Zakopane, Poland, 2000: 331-338
59 T. Zielinska, J. Heng. Development of a Walking Machine: Mechanical Design and Control Problems. Mechatronics. 2002 (12): 737-754
60 R. A. Brooks. A Robust Layered Control System for a Mobile Robot. IEEE Journal of Robotics and Automation. 1986, RA-2(1): 14-23
61 E. Celaya, J. L. Albarral. Implementation of a Hierarchical Walk Controller for the LAURON III Hexapod Robot. The International Conference on Climbing and Walking Robots, Catania, Italy, 2003: 409-416
62 J. M. Porta, E. Celaya. Reactive Free-gait Generation to Follow Arbitrary Trajectories with a Hexapod Robot. Robotics and Autonomous Systems. 2004, 47(4): 187-201
63 E. Celaya, J. M. Porta. A Control Structure for the Locomotion of a Legged Robot on Difficult Terrain. IEEE Robotics and Automation Magazine. 1998, 5(2): 43-51.
64 E. Celaya, J. M. Porta. Control of a Six-legged Robot Walking on Abrupt Terrain. The IEEE International Conference on Robotics and Automation, Minneapolis, USA, 1996: 2731-2736
65 O. Janrathitikarn, L. N. Long. Gait Control of a Six-legged Robot on Unlevel Terrain Using a Cognitive Architecture. The IEEE Aerospace Conference, Big Sky, USA, 2008: 70-78
66顾冬雷,陈卫东,席裕庚.移动机器人条件反射能力的实现.机器人. 2001, 23(2): 123-126
67 M. S. Erden, K. Leblebiciolu. Multi Legged Walking in Robotics and Dynamic Gait Pattern Generation for a Six-legged Robot with Reinforcement Learning. In Mobile Robots: New Research. New York: Nova. 2005
68 J. M. Porta, E. Celaya. Efficient Gait Generation Using Reinforcement Learning. The International Conference on Climbing and Walking Robots, Karlsruhe, Germany, 2001: 411-418
69 M. S. Erden, K. Leblebicioglu. Free Gait Generation with Reinforcement Learning for a Six-legged Robot. Robotics and Autonomous Systems. 2008, 56(3): 199-212
70 J. Dean, G. Wendler. Stick Insect Locomotion on a Walking Wheel: Inter-leg Coordination of Leg Position. Journal of Experimental Biology. 1983, 103: 75-94
71 K. G. Pearson, R. Franklin. Characteristics of Leg Movements and Patterns of Coordination in Locusts Walking on Rough Terrain. Journal of Robotics Research. 1984, 3(2): 101-112
72 Bettina Blasing. Crossing Large Gaps: A Simulation Study of Stick Insect Behavior. Adaptive Behavior. 2006, 14(3): 265-285
73 H. Cruse. The Control of the Anterior Extreme Position of the Hind leg of a Walking Stick Insect, Carausius Morosus. Physiological Entomology. 1979, 4: 121-124
74 H. Cruse. What Mechanisms Coordinate Leg Movement in Walking Arthropods. Trends in Neuroscience. 1990, 13: 15-20
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