跳跃机器人轨迹规划及控制仿真研究
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摘要
跳跃机器人具有运动灵活度高,环境适应力强等优点,可广泛应用于考古探测、星际探索、军事侦察、地质勘探、森林防护、抢险救灾以及反恐救援等地势复杂的情况。近三十年来,对跳跃机器人的研究大都集中于腿型跳跃机器人。这种跳跃机器人仿生度高,运动灵活性好,但是由于其高度非线性和强耦合特性,增加了运动分析和控制的难度。
本文将跳跃机器人抽象成一个平面冗余机器人,分阶段分析了跳跃机器人运动学和动力学特性。通过引入虚拟被动关节,建立了跳跃机器人浮动基模型,利用拉格朗日方法推导了跳跃运动统一的动力学方程,从约束变换角度区分运动的不同阶段,并给出了离地的判断条件。
根据跳跃机器人起跳阶段和落地阶段任务空间的要求,利用可变五次多项式分别规划了跳跃机器人起跳阶段和落地阶段任务空间轨迹。利用梯度投影法求解起跳阶段关节空间轨迹,并从速度可操作性和动能最优方面对关节空间轨迹进行优化。
在分析腾空相跳跃机器人的欠驱动特性基础上,推导了跳跃机器人等效全驱动模型。并利用梯度投影法求解主动关节轨迹。针对求解过程易出现动力学奇异这一问题做出了探讨。
综合运用MATLAB/Simulink和MATLAB/SimMechanics仿真平台,建立了跳跃机器人控制器模型和机构模型,对跳跃机器人进行了关节空间轨迹跟踪控制仿真分析。
利用跳跃机器人浮动基模型,建立了跳跃机器人状态空间模型。采用设计趋近律的方法在任务空间上设计滑模控制器,直接对任务空间轨迹进行控制。在MATLAB /Simulink和MATLAB/SimMechanics仿真环境下对控制系统进行仿真,检验了控制算法的有效性。
本论文的研究工作,对腿式跳跃机器人的建模、轨迹规划和控制具有一定的参考价值。
Hopping robot with the advantages of high kinetic dexterity and environmental adaptability can be widely applied to the complex and rough ground environment, such as the archaeological exploration, interstellar exploration, military reconnaissance, geological prospecting, forest protection, rescue and counter-terrorism relief etc. In recent 30 years, the research on hopping robot is mostly concentrated in the legged-hopping robot. This kind of hopping robot has the advantage of high Bionic and dexterity, but its highly nonlinear and strong coupling characteristics increase the difficulty of motion analysis and control.
In this dissertation, the hopping robot is seen as a plane redundant robot. The kinematics and dynamic characteristics are analyzed by phases. The floating base model of hopping robot has been established by introducing the virtual passive joint. The unified dynamics equation of hopping robot including flight phase and stance phase has been achieved using Lagrange method based on the floating base, and the phases are distinguished by the difference of constraint. At the same time, the judging condition for the takeoff of hopping robot has been presented.
According to the requirement of task space in takeoff phase and landing phase, using the variable parameter quintic polynomial the trajectory planning of hopping robot in task space has been worked. Using the Gradient Projection Method the trajectory of joint space has been computed, and the trajectory optimization has also been worked.
After analyzing the underactuated characteristics of hopping robot in flying phase, the equivalent full-drive model of hopping robot has been developed. Using the Gradient Projection Method, the actuate joint trajectory has been computed. According to the problem of that the dynamic singularity is easily appeared during the computation, a discussion has been developed.
By the comprehensive use of MATLAB/Simulink and MATLAB/SimMechanics simulation platform, the controller model and mechanics model of hopping robot are established, and the simulation of trajectory tracking in the joint space has been worked.
Using the floating base model, the state space model of hopping robot has been developed.
By design the reaching law, the silding mode controller has been designed in then task space, which can control the trajectory in task space directly. The control algorithm has been examined by the simulation in MATLAB/Simulink an MATLAB/SimMechanics.
The study of this dissertation provides some reference value for the modeling, trajectory planning and control of hopping robot.
本文将跳跃机器人抽象成一个平面冗余机器人,分阶段分析了跳跃机器人运动学和动力学特性。通过引入虚拟被动关节,建立了跳跃机器人浮动基模型,利用拉格朗日方法推导了跳跃运动统一的动力学方程,从约束变换角度区分运动的不同阶段,并给出了离地的判断条件。
根据跳跃机器人起跳阶段和落地阶段任务空间的要求,利用可变五次多项式分别规划了跳跃机器人起跳阶段和落地阶段任务空间轨迹。利用梯度投影法求解起跳阶段关节空间轨迹,并从速度可操作性和动能最优方面对关节空间轨迹进行优化。
在分析腾空相跳跃机器人的欠驱动特性基础上,推导了跳跃机器人等效全驱动模型。并利用梯度投影法求解主动关节轨迹。针对求解过程易出现动力学奇异这一问题做出了探讨。
综合运用MATLAB/Simulink和MATLAB/SimMechanics仿真平台,建立了跳跃机器人控制器模型和机构模型,对跳跃机器人进行了关节空间轨迹跟踪控制仿真分析。
利用跳跃机器人浮动基模型,建立了跳跃机器人状态空间模型。采用设计趋近律的方法在任务空间上设计滑模控制器,直接对任务空间轨迹进行控制。在MATLAB /Simulink和MATLAB/SimMechanics仿真环境下对控制系统进行仿真,检验了控制算法的有效性。
本论文的研究工作,对腿式跳跃机器人的建模、轨迹规划和控制具有一定的参考价值。
Hopping robot with the advantages of high kinetic dexterity and environmental adaptability can be widely applied to the complex and rough ground environment, such as the archaeological exploration, interstellar exploration, military reconnaissance, geological prospecting, forest protection, rescue and counter-terrorism relief etc. In recent 30 years, the research on hopping robot is mostly concentrated in the legged-hopping robot. This kind of hopping robot has the advantage of high Bionic and dexterity, but its highly nonlinear and strong coupling characteristics increase the difficulty of motion analysis and control.
In this dissertation, the hopping robot is seen as a plane redundant robot. The kinematics and dynamic characteristics are analyzed by phases. The floating base model of hopping robot has been established by introducing the virtual passive joint. The unified dynamics equation of hopping robot including flight phase and stance phase has been achieved using Lagrange method based on the floating base, and the phases are distinguished by the difference of constraint. At the same time, the judging condition for the takeoff of hopping robot has been presented.
According to the requirement of task space in takeoff phase and landing phase, using the variable parameter quintic polynomial the trajectory planning of hopping robot in task space has been worked. Using the Gradient Projection Method the trajectory of joint space has been computed, and the trajectory optimization has also been worked.
After analyzing the underactuated characteristics of hopping robot in flying phase, the equivalent full-drive model of hopping robot has been developed. Using the Gradient Projection Method, the actuate joint trajectory has been computed. According to the problem of that the dynamic singularity is easily appeared during the computation, a discussion has been developed.
By the comprehensive use of MATLAB/Simulink and MATLAB/SimMechanics simulation platform, the controller model and mechanics model of hopping robot are established, and the simulation of trajectory tracking in the joint space has been worked.
Using the floating base model, the state space model of hopping robot has been developed.
By design the reaching law, the silding mode controller has been designed in then task space, which can control the trajectory in task space directly. The control algorithm has been examined by the simulation in MATLAB/Simulink an MATLAB/SimMechanics.
The study of this dissertation provides some reference value for the modeling, trajectory planning and control of hopping robot.
引文
[1]Matsuoka K., A mechanical model of repetitive hopping movements [J]. Biomec-hanisms,1980,5(2):251-258.
[2]Raibert M H. Legged Robots that Balance [M]. Cambridge:MIT Press, 1986:45-8.
[3]Masaki Yamakita, Yasuhito Omagari, Yasuaki Taniguchi. Jumping Cat Robot with kicking a Wall [J]. Journal of the Robotics Society of Japan,1994:934-938.
[4]Keisuke Arikawa, Tsutomu Mita, Design of Multi-DOF Jumping Robot [C]. Proceedings of the 2002 IEEE International Conference on Robotics & Automation,2002:312-319.
[5]Sang-Ho Hyon, Naoto Yokoyama, Takashi Emura. Back Handspring Robot-Target Dynamics-Based Control [C]. Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems,2004:248-253.
[6]Matthew C Birch, Roger D Quinn, Geon Hahm, et al.. Design of a cricket microrobot [C]. Proceedings of the 2000 IEEE International Conference on Robotics & Automation. San Francisco CA. April 2000:1109-1114.
[7]Laksanacharoen, S. Pollack, A. J. Nelson, G. M. Quinn, R. D. Ritzmann, R. E. Biomechanics and simulation of cricket for microrobot design. IEEE Conf. on Robotics and Automation. April 2000,2:1088-1094.
[8]S. H. Hyon, T. Mita. Development of a biologically inspired hopping robot-"kenken" [C]. Proceedings of the 2002 IEEE international conference on robotics automation. Washington, DC.,2002.
[9]Shuuji, Kajiata. A hop towards running humanoid biped [C]. Proceedings of the 2004 IEEE international conference on robotics & automation. New Orieans, LA. April 2004.
[10]James P. S. The mechanics of and robotic design for quadrupedal galloping [D]. Ohio:the Ohio State University,2001.
[11]Nelson. G.M., Quinn. R. D.. Posture Control of a Cockroach-like Robot. Video Proc. IEEE Int. Conf. Robot. Belgium,1999:9-14.
[12]Fumitaka. KIKUCHI, Yusuke OTA, Shigeo HIROSE. Basic Performance Exp-eriments for Jumping Quadruped [C]. Proceedings of the 2003 IEEE RSJ. In Conference on Intelligent Robots and Systems,2003.
[13]HC Wong, DE Orin. Dynamic Control of a Quadruped Standing Jump [C]. IEEE International Conference on Robotics and Automation,1993:346-351.
[14]Ryuma Niiyama, Akihiko Nagakubo, Yasuo Kuniyoshi. A Bipedal Jumping and Landing Robot with an Artificial Musculoskeletal System [C]. IEEE International Conference on Robotics and Automation Roma, Italy,2007:10-14.
[15]杨煜普,耿涛,郭毓.一种新型翻转跳跃运动机器人的运动结构与轨迹规划[J].上海交通大学学报.2003,37(7)：1110-1113.
[16]李涛.一种仿青蛙跳跃机器人机构设计与运动分析[D].北京：北方工业大学,2008：25.
[17]何广平谭晓兰张向慧.双臂弹性单腿机器人的垂直跳跃控制[J].机械工程学报,2007,43(5)：44-49.
[18]马利娥.仿袋鼠机器人跳跃运动机理的研究[D],西安：西北工业大学,2005：15.
[19]关山原野.仿生机器蛙跳跃机理分析及运动仿真[D].哈尔滨：哈尔滨工业大学,2007：25-42.
[20]余杭杞.仿蝗虫四足跳跃机器人的机构设计和运动性能分析[D].哈尔滨：哈尔滨工业大学,2006：22-42.
[21]Saranli, U., Schwind, W.J., Koditschek, D.E.Toward the control of a multi-jointed monopod runner[C]. In IEEE int. Conf. on robotics and automation.1998: 2767-2682.
[22]Kajita, S., Kanehiro, F. etc. Resolved momentum control:humanoid motion planning based on the linear and angular momentum[C]. in Proc. of the IEEE Int. Conf. on Intelligent Robots and Systems.2003:1644-1650.
[23]Yasutaka Fujimoto. Trajectory Generation of Biped Running Robot with Minimum Energy Consumption[C]. Proceedings of the 2004 IEEE International Conference on Robotics & Automation New Orleans, IA-April 2004:3803-3808.
[24]J. V. Albro, J. E. Bobrow. Optimal Motion Primitives for a 5 DOF Experimental Hopper[C]. Proceedings of the 2001 IEEE International Conference on Robotics & Automation, May 21-26,2001:3630-3635.
[25]Tomoya TAKAHASHI, Masaki YAMAKITA. An Optimization Approach for Underactuated Running Robot. SICE-ICASE International Joint Conference, Oct. 18-21,2006. Bexco, Busan, Korea:3505-3510.
[26]Victor Nunez, S. Drakunov. Control Strategy for Planar Vertical Jump. Advanced Robotics,2005. ICAR'05. Proceedings 12th. International Conference on,2005: 849-855.
[27]Sugihara, T., Nakamura Y.. Contact phase invariant control for humanoid robot based on variable impedant inverted pendulum model[C], Proc. of the IEEE International Conference on Robotics and Automation, September 2003:51-56.
[28]SHO SAKAINO, KOUHEI OHNISHI. Trajectory Planning and Control of One-Legged Hopping Robot at Thrusting Phase[J]. Electrical Engineering in Japan,169(2),2009:884-889.
[29]Eijira Ohashi, Kouhei Ohnishi. Variable Compliance Control Based on Soft-Landing Trajecory for Hopping Robot[C]. The 30th Conference of the IEEE Industrial Electronics Society, November 2-5,2004, Busan, Korea:117-120.
[30]Sho Sakaino, Kouhei. Sliding Model Control Based on Position Control for Contact Motion [C]. Proc. of the IEEE International Conference on Robotics and Automation,2006:170-175.
[31]Sho Sakaino, Kouhei. An Approach for Force Control of Redundant Robots under Unknown Environment [C]. Proc. of the IEEE International Conference on Rob-otics and Automation.2008:1312-1317.
[32]Sho Sakaino, Kouhei. Dynamic Force Control Having No Singular Point on Momentum Control System[C]. Proceeding of International Conference on Mechatronics.2007:1-6.
[33]魏航信,刘明治.拟人机器人矢状面跑步运动规划[J].西安电子科技大学学报(自然科学版).2006,33(3)：376-380.
[34]徐兆红.腿式跳跃机器人运动规划与稳定性恢复研究[D].上海：上海交通大学.2009.
[35]徐兆红,吕恬生.跳跃机器人模糊自适应轨迹跟踪控制[J].系统仿真学报.2008,20(23)：6455-6457.
[36]王瑜,何广平.双臂单腿跳跃机器人的动力学建模与仿真[J].北方工业大学学报.2007,19(3)：31-38.
[37]陆震.冗余自由度原理及应用[M].北京：机械工业出版社,2007：52-59.
[38]叶敏.肖龙翔.分析力学[M].天津：天津大学出版社.2001：2-13 13-20.
[39]Richard M. Murray, Zexiang Li, S., Shankar Sastry. A Mathematical Introduction to Robotic Manipulation[M]. Florida:CRC Press,1994:177-179.
[40]李鲁亚.冗余自由度机器人控制研究[D].北京：北京航空航天大学研究生院.
[41]Dynamic Manipulability of Robotics Mechanisms[C]. Proc. of IEEE Int. conf. on Robotics and Automation,1985:1033-1038.
[42]何广平,陆震,王凤翔.欠驱动余度机械臂的非完整冗余特征研究[J].宇航学报.2005,26(2)：143-147.
[43]陆震.冗余自由度机器人原理及应用[M].北京：机械工业出版社.2006.10：130-133.
[44]王汉磊.机器人运动学奇异与冗余运动规划一阶方法的研究[D].哈尔滨：哈尔滨工业大学,2006：6-19.
[45]董玉红,杨清梅.机械控制工程基础[M].哈尔滨：哈尔滨工业大学出版社,2003：17-178.
[46]张立勋,董玉红.机电系统仿真与设计[M].哈尔滨：哈尔滨工程大学出版社,2006：134-154.
[47]刘金琨.先进PID控制MATLAB仿真[M].北京：电子工业出版社,2005：1.
[48]刘金琨.滑模变结构控制MATLAB仿真[M].北京：清华大学出版社.2005：1.
[49]张晓字,苏宏业.滑模变结构控制理论进展综述[J].化工自动化及仪表,2006,33(2)：1-8.
[2]Raibert M H. Legged Robots that Balance [M]. Cambridge:MIT Press, 1986:45-8.
[3]Masaki Yamakita, Yasuhito Omagari, Yasuaki Taniguchi. Jumping Cat Robot with kicking a Wall [J]. Journal of the Robotics Society of Japan,1994:934-938.
[4]Keisuke Arikawa, Tsutomu Mita, Design of Multi-DOF Jumping Robot [C]. Proceedings of the 2002 IEEE International Conference on Robotics & Automation,2002:312-319.
[5]Sang-Ho Hyon, Naoto Yokoyama, Takashi Emura. Back Handspring Robot-Target Dynamics-Based Control [C]. Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems,2004:248-253.
[6]Matthew C Birch, Roger D Quinn, Geon Hahm, et al.. Design of a cricket microrobot [C]. Proceedings of the 2000 IEEE International Conference on Robotics & Automation. San Francisco CA. April 2000:1109-1114.
[7]Laksanacharoen, S. Pollack, A. J. Nelson, G. M. Quinn, R. D. Ritzmann, R. E. Biomechanics and simulation of cricket for microrobot design. IEEE Conf. on Robotics and Automation. April 2000,2:1088-1094.
[8]S. H. Hyon, T. Mita. Development of a biologically inspired hopping robot-"kenken" [C]. Proceedings of the 2002 IEEE international conference on robotics automation. Washington, DC.,2002.
[9]Shuuji, Kajiata. A hop towards running humanoid biped [C]. Proceedings of the 2004 IEEE international conference on robotics & automation. New Orieans, LA. April 2004.
[10]James P. S. The mechanics of and robotic design for quadrupedal galloping [D]. Ohio:the Ohio State University,2001.
[11]Nelson. G.M., Quinn. R. D.. Posture Control of a Cockroach-like Robot. Video Proc. IEEE Int. Conf. Robot. Belgium,1999:9-14.
[12]Fumitaka. KIKUCHI, Yusuke OTA, Shigeo HIROSE. Basic Performance Exp-eriments for Jumping Quadruped [C]. Proceedings of the 2003 IEEE RSJ. In Conference on Intelligent Robots and Systems,2003.
[13]HC Wong, DE Orin. Dynamic Control of a Quadruped Standing Jump [C]. IEEE International Conference on Robotics and Automation,1993:346-351.
[14]Ryuma Niiyama, Akihiko Nagakubo, Yasuo Kuniyoshi. A Bipedal Jumping and Landing Robot with an Artificial Musculoskeletal System [C]. IEEE International Conference on Robotics and Automation Roma, Italy,2007:10-14.
[15]杨煜普,耿涛,郭毓.一种新型翻转跳跃运动机器人的运动结构与轨迹规划[J].上海交通大学学报.2003,37(7)：1110-1113.
[16]李涛.一种仿青蛙跳跃机器人机构设计与运动分析[D].北京：北方工业大学,2008：25.
[17]何广平谭晓兰张向慧.双臂弹性单腿机器人的垂直跳跃控制[J].机械工程学报,2007,43(5)：44-49.
[18]马利娥.仿袋鼠机器人跳跃运动机理的研究[D],西安：西北工业大学,2005：15.
[19]关山原野.仿生机器蛙跳跃机理分析及运动仿真[D].哈尔滨：哈尔滨工业大学,2007：25-42.
[20]余杭杞.仿蝗虫四足跳跃机器人的机构设计和运动性能分析[D].哈尔滨：哈尔滨工业大学,2006：22-42.
[21]Saranli, U., Schwind, W.J., Koditschek, D.E.Toward the control of a multi-jointed monopod runner[C]. In IEEE int. Conf. on robotics and automation.1998: 2767-2682.
[22]Kajita, S., Kanehiro, F. etc. Resolved momentum control:humanoid motion planning based on the linear and angular momentum[C]. in Proc. of the IEEE Int. Conf. on Intelligent Robots and Systems.2003:1644-1650.
[23]Yasutaka Fujimoto. Trajectory Generation of Biped Running Robot with Minimum Energy Consumption[C]. Proceedings of the 2004 IEEE International Conference on Robotics & Automation New Orleans, IA-April 2004:3803-3808.
[24]J. V. Albro, J. E. Bobrow. Optimal Motion Primitives for a 5 DOF Experimental Hopper[C]. Proceedings of the 2001 IEEE International Conference on Robotics & Automation, May 21-26,2001:3630-3635.
[25]Tomoya TAKAHASHI, Masaki YAMAKITA. An Optimization Approach for Underactuated Running Robot. SICE-ICASE International Joint Conference, Oct. 18-21,2006. Bexco, Busan, Korea:3505-3510.
[26]Victor Nunez, S. Drakunov. Control Strategy for Planar Vertical Jump. Advanced Robotics,2005. ICAR'05. Proceedings 12th. International Conference on,2005: 849-855.
[27]Sugihara, T., Nakamura Y.. Contact phase invariant control for humanoid robot based on variable impedant inverted pendulum model[C], Proc. of the IEEE International Conference on Robotics and Automation, September 2003:51-56.
[28]SHO SAKAINO, KOUHEI OHNISHI. Trajectory Planning and Control of One-Legged Hopping Robot at Thrusting Phase[J]. Electrical Engineering in Japan,169(2),2009:884-889.
[29]Eijira Ohashi, Kouhei Ohnishi. Variable Compliance Control Based on Soft-Landing Trajecory for Hopping Robot[C]. The 30th Conference of the IEEE Industrial Electronics Society, November 2-5,2004, Busan, Korea:117-120.
[30]Sho Sakaino, Kouhei. Sliding Model Control Based on Position Control for Contact Motion [C]. Proc. of the IEEE International Conference on Robotics and Automation,2006:170-175.
[31]Sho Sakaino, Kouhei. An Approach for Force Control of Redundant Robots under Unknown Environment [C]. Proc. of the IEEE International Conference on Rob-otics and Automation.2008:1312-1317.
[32]Sho Sakaino, Kouhei. Dynamic Force Control Having No Singular Point on Momentum Control System[C]. Proceeding of International Conference on Mechatronics.2007:1-6.
[33]魏航信,刘明治.拟人机器人矢状面跑步运动规划[J].西安电子科技大学学报(自然科学版).2006,33(3)：376-380.
[34]徐兆红.腿式跳跃机器人运动规划与稳定性恢复研究[D].上海：上海交通大学.2009.
[35]徐兆红,吕恬生.跳跃机器人模糊自适应轨迹跟踪控制[J].系统仿真学报.2008,20(23)：6455-6457.
[36]王瑜,何广平.双臂单腿跳跃机器人的动力学建模与仿真[J].北方工业大学学报.2007,19(3)：31-38.
[37]陆震.冗余自由度原理及应用[M].北京：机械工业出版社,2007：52-59.
[38]叶敏.肖龙翔.分析力学[M].天津：天津大学出版社.2001：2-13 13-20.
[39]Richard M. Murray, Zexiang Li, S., Shankar Sastry. A Mathematical Introduction to Robotic Manipulation[M]. Florida:CRC Press,1994:177-179.
[40]李鲁亚.冗余自由度机器人控制研究[D].北京：北京航空航天大学研究生院.
[41]Dynamic Manipulability of Robotics Mechanisms[C]. Proc. of IEEE Int. conf. on Robotics and Automation,1985:1033-1038.
[42]何广平,陆震,王凤翔.欠驱动余度机械臂的非完整冗余特征研究[J].宇航学报.2005,26(2)：143-147.
[43]陆震.冗余自由度机器人原理及应用[M].北京：机械工业出版社.2006.10：130-133.
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