Research of Mammal Bionic Quadruped Robots: a Review

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1 Research of Mammal Bionic Quadruped Robots: a Review Yibin Li, Bin Li, Jiuhong Ruan and Xuewen Rong, Member, IEEE Abstract This paper focuses on the mammal bionic quadruped robots. The main challenge in this field is how to design the highly dynamical and high payload quadruped robots. This paper firstly introduces the history of bionic quadruped robots, particularly the landmark quadruped robots. Then the state-of-the art of drive mode for quadruped robots is reviewed. Subsequently, the development trend of quadruped robots is described. Based on the state-of-the art of quadruped robots, the technical difficulties of bionic quadruped robots are briefly reviewed. And the hydraulic quadruped robot developed in Shandong University is introduced. Finally, the summary and future work of the quadruped robots is given. I. INTRODUCTION HE need for mobile robots instead of human to work in some complex and dangerous environments has attracted Tmore and more attention, such as underground mine, nuclear power station, and war against terrorism. Generally, the mobile robots can be classified into three types: air robots, underwater robots and ground robots. The ground robots are developed mostly with tracks or wheels. Although wheeled and tracked robots can work well in even surface, most of them cannot work in uneven surface. In other words, only a portion of the earth s landmass is accessible for the existing ground robots. Compared with the wheeled and tracked robots, legged robots have the potential to walk in a much wider variety of terrains just like the fact that biological legged animals can access nearly all of the earth s land surfaces. For example, the gazelle has the efficient dynamical locomotion performance even in highly complex environments. Consequently, this potential has motivated a lot of research on legged robots in recent years. And legged robots that can go to the places that animals can now reach should be constructed for real applications. Despite a great number of achievements in robotics field, legged robots still lag far behind the capabilities of their bionics [1, 2]. Legged robots are classified into mammal robots and reptile robots based on the mechanical structures. Compared with the reptilian robots, the mammal robots basically vertical leg orientation may be regarded as weight carrying adaptation. The Manuscript received April 20, This work is supported by the Independent Innovation Foundation of Shandong University under grant no. 2009JC010 and National High-tech R&D Program of China. Yibin Li, Bin Li and Xuewen Rong are with the School of Control Science and Engineering, Shandong University. Bin Li is also with School of Science, Shandong Polytechnic University. Jiuhong Ruan is with Advanced Vehicle and Robot Institute, Shandong Jiaotong University. Yibin Li is corresponding author ( liyb@ sdu.edu.cn). mammal robots can carry much more payload in an efficient way. The mammal robots with joint actuators have good walking speed and transportation power. Consequently, the research of bionic robots based on mammal animals becomes an important development direction in robotics field. Legged robots have been built with one, two, three, four and possibly more legs. An even number of legs which allows efficient gaits and stability performance is almost universal [3]. Among legged robots, the quadruped robots have good mobility and stability of locomotion, while the typical biped robots lack the locomotion stability. The quadruped robot also is a good choice from the point of view of a system and controller design. On the other hand, four legs are less complicated to construct and maintain than six ones. Quadruped robots are more versatile than wheeled and tracked robots, and more stable than biped robots. Many researchers and groups have been working on quadruped robots with biologically inspired locomotion of dynamical gaits, robot balancing skills and the capability of high payload. In general, in order to improve dynamic stability and to increase the walking speed as well as the transportation power of the quadruped robots, hydraulic actuators with large bandwidth and high output power are needed. The robot control system, which manages the dynamics of quadruped robot behavior, gait generation and transition method also should be studied and solved in the future. This paper is organized as follows: The history of mammal bionic quadruped robots and the development trend of drive mode are reviewed in Section II. Section III describes the development trend of quadruped robots. Then, the technology difficulties of quadruped robots are analyzed in Section IV. The hydraulic quadruped robot being developed in Shandong University in China is introduced in Section V. The last section of this paper is the summary and future work of the quadruped robots. II. HISTORY OF MAMMAL QUADRUPED ROBOTS This section reviews the history of the bionic quadruped robots with joint actuators. We firstly focus on the current development of quadruped robots based on bionics of mammal animals. And then the development trend of the drive mode of quadruped robots, especially the hydraulic actuators which is a new-growing drive mode with improved dynamical performance and payload capacity, is reviewed in detail in this section. A. History of mammal bionic quadruped robots The investigation of quadruped robots is from 20 th century 60 s while the study of dynamic locomotion performance for /11/$26.00 c 2011 IEEE 166

2 quadruped robots began from the 1980 s. Marc Raibert and his colleagues have made great success in dynamic legged locomotion of one, two, four legged robots. In the early 1960 s, many scientists and researchers abroad were devoted in researching the legged robots. In 1960, linkage mechanisms included four-bar linkages, cam linkage, pantograph mechanisms for locomotion of legged robot was proposed by Shigley. The motion of the legs was controlled by a set of double-rocker linkages [4]. In 1966, McGhee and Frank built quadruped dubbed the Phoney Pony. This was the first legged vehicle to walk autonomously under full computer control. Each leg of this quadruped robot had two degrees of freedom (DOFs) system and performed the simple crawling locomotion as well as the diagonal trot depending on the selected state diagram. The Phoney Pony robot has great significance since it inspired McGhee to build new machines, which also played an important role in the history of walking robots: the OSU hexapod and the Adaptive Suspension Vehicle (ASV) [5]. In the early 1980 s, Marc Raibert of Massachusetts Institute of Technology (MIT), and H. Miura and I. Shimoyama of the University of Tokyo carried out a systemic research on the mammal quadruped robot firstly. Marc Raibert built planar and three-dimensional one-legged hopping machines. Based on the Raibert s three controlling principle of hopping machine, biped and quadruped robots with prismatic legs which can run and jump were subsequently built. This was a milestone of the motion control of dynamic gaits for quadruped robots [6]. During , the dynamic walking quadruped robots, Collie-1 and Collie-2 generations, had been constructed and further studied under the supervision of Professor Miura and Professor Shimoyama in the University of Tokyo. These robots could achieve the trotting and pacing dynamic walking gaits and transition of between trotting and pacing gaits [7]. Strictly speaking, although TITAN series quadruped robots are not belonging to the mammal ones, it is also an important milestone in the development history of robotics. TITAN III is a quadruped robot with three dimensional pantograph mechanism legs in the TITAN series. It is equipped with posture sensor and whisker sensors, and is loaded with an intelligent gait control system for making decisions in terms of the sensor information and realizing terrain adaptive static walk [8]. With the further development of quadruped robots, the four-legged walking machine named BISAM was generated by R. Dillmann and his researching team in Germany. An adaptive control approach based on coupled neural oscillators was used to model periodic locomotion of robot BISAM, and realize a robust control method based on the biologically inspired adaptive control architecture for achieving dynamically stable motion in the experimental platform robot BISAM [9]. In 1999, based on Central Pattern Generators (CPGs), Hiroshi Kimura and his colleagues in Kyoto Institute of Technology investigated the dynamic walking approach for quadruped robots. The quadruped robot Patrush and the following robots of Tekken series were developed. Among the Tekken series, the self-contained quadruped robot Tekken II was actuated by electric motors, mechanical springs and compliance to the joints and could realize dynamic walking using CPGs and reflexes [10]. Kimura also started the research of the quadruped robot Kotetsu to challenge the general controller for quadruped locomotion with adaptive dynamic walking using phase modulations based on leg loading/unloading in 2009 [11]. In 1999, Scout II quadruped robot, a dynamically stable running quadruped robot with a very simple mechanical, was designed to explore the dynamic gaits of mammal animals by Martin Buehler at Ambulatory Robotics Lab (ARL) of McGill University [12]. A bionic quadruped walking robot platform called Warp1 for complex terrains has been developed in the Royal Institute of Technology in Stockholm since The purpose of the robot platform is to study the automatically walking in complicated environment and to realize the static and dynamic walking locomotion [13]. The KOLT robot was designed by Kenneth Waldron and his group at Stanford University in collaboration with Ohio State University in around 2001 [14]. Marc Raibert and his colleagues founded Boston Dynamics Corporation (BDI) in They restarted the research project of bionic quadruped robot from Moreover, the first generation of quadruped robot in 2005 is named as BigDog. The second generation of BigDog was developed in 2008, as shown in Fig. 1. The second generation BigDog is 1m long, 0.7m height and weighed about 75 kg. Each leg of the quadruped robot had four active degrees of freedom with rotational joints powered by hydraulic cylinders and one passive linear joint in the foot based on the pneumatic spring. BigDog is able to walk up and down 30 inclines, trot at speed up to 1.8m/s, carry over 153 kg of payload, walk through forest, snow, recover balance after sliding on ice or after kicks from the side [15]. Fig. 1. BigDog robot. In December of 2009, BDI has been awarded a contract by the Defense Advanced Research Projects Agency (DARPA) to develop LS3, the first Legged Squad Support System. LS3 is a 2011 IEEE 5th International Conference on Robotics, Automation and Mechatronics (RAM) 167

3 dynamic robot designed to go anywhere Soldiers and Marines go on foot. Each LS3 will carry up to 400 lbs of gear and enough fuel for missions covering 20 miles and lasting 24 hours. LS3 will not need a driver, because it will automatically follow a leader using computer vision or travel to designated locations using sensing and GPS. BDI plans for the development to take 30 months, with a working prototype ready by 2012 [16]. On March 1, 2011, with the financial aid of DARPA, BDI will also develop cheetah robot. The cheetah robot will have four legs, a flexible spine, an articulated head/neck, and perhaps a tail. It will be able to run faster than any existing legged robot or human runner, make tight, zigzagging turns in order to chase or evade, be able to accelerate very rapidly from a standstill, and stop just as quickly [17]. This will be a paramount milestone in the development of robotics if the prototype of cheetah robot is fulfilled. Recently, the researchers of Korea Institute of Industrial Technology and Rotem Company develop a hydraulic actuated quadruped walking robot. All joints of leg of the robot are actuated by hydraulic rotary actuator carry heavy payloads and to move fast on uneven terrain. This type robot has achieved the basic trotting gait in even terrain of laboratory environment [18, 19]. Combining hydraulic with electric actuators, researchers of the Italian Institute of Technology is currently constructing a quadruped robot (called HyQ) for performing highly dynamic tasks like jumping, hopping and running [20]. So far, the robot HyQ just has realized the position control approach of single leg with linear hydraulic actuators. Besides the development of robot abroad, Sunpei Ma of Shanghai Jiaotong University developed a four legged robot named JTUWM-III for the first time at the domestic in Each leg of JTUWM-III robot has three active joints and a compliant joint. DC servo motor was used to actuate the each active joint [21]. The Biobot (biologically inspired robot) was developed by Xiuli Zhang and her colleagues at Tsinghua University in She proposed a holosymmetric CPG topological network based on the improved Matsuoka s oscillator model. Furthermore, the rhythmic motion and transitions of different gaits were realized. The locomotion ability of Biobot in real environments was improved based on the CPG model [22]. In 2006, Xuedong Chen and his colleagues developed a modular robot called MiniQuad which could be reconfigured into variety configurations, including quadruped and hexapod configurations for different tasks by changing the layout of modules [23, 24]. Besides, other quadruped robots also have been developed by some research institutions and universities, including the mammal quadruped robot named TIM1 reported by Institute of Intelligent Machine, Chinese Academy of Science, the quadruped robot developed by Northwestern Polytechnical University and big quadruped robot with electric drives researched by Institute of Automation Chinese Academy of Science. B. The drive mode for quadruped robots In general, the actuators in robotics include electric, pneumatic and hydraulic actuators. Electric motors are the most common actuators in the field of robotics due to their technological advances and cheapness. Therefore, reduction gears are one of the weakest elements of an electric motor assembly, and many moving parts of them prone to wear. Pneumatic actuators are similar to hydraulic actuators except for that they use compressed gas to provide pressure instead of liquid. Pneumatic systems respond very quickly. But the compressibility of air means that precise position control of the systems is impossible. The hydraulic actuators are driven by an oil pressurized fluid of working with high pressures of around 21 MPa (can reach up to 70 MPa in some systems). These results make the hydraulic actuators have very high power-to-weight ratios, high bandwidth, fast response and intrinsic compliance to a certain degree [25]. Hydraulic actuators can be very effective for high power applications. In recent years, the hydraulic actuated quadruped robots for highly dynamic and heavy payload tasks have been developing by many researchers since their properties are very suitable for highly dynamic legged robots. BigDog developed by Raibert et al. at Boston Dynamics is the most advanced hydraulic actuated quadruped robot [15]. Many other hydraulic quadruped robots are also developed or under development. For example, p2, a hydraulically driven quadruped robot, is under development to be used in military environment in Korea [18, 19]. The researchers of Italian Institute of Technology are constructing HyQ robot with a combination of hydraulic and electric actuators to perform highly dynamic tasks like jumping, hopping and running [20]. III. DEVELOPING TREND OF QUADRUPED ROBOTS The developing trend of bionic quadruped robots is mainly driven by the mode of engine-hydraulic actuated power for improving the power weight ratio and realizing the characteristics of fast response, strong robust stability and long range walking ability. The key technologies in environmental identification of complex terrains, information fusion, gait generation, feedback regulation of position-force, trajectory planning of foot and body for quadruped robot and stability control strategy, etc. should be studied. This development may promote the bionic quadruped robots into practical applications. The specific development trends are as follows: 1) Bionic: bionic form and construction, bio-mimetic gaits After thousands years of evolution, the mammalian animal s skeletal configurations and gaits have achieved the highest level of adaptation to the environments with their unique walking mode. Therefore, the mammal s body structure, freedom assignment, and joints configurations are the best references for the design of bionic legged robots. In order to design bionic quadruped robots with mammalian animal characteristics of IEEE 5th International Conference on Robotics, Automation and Mechatronics (RAM)

4 more flexible locomotion, higher power supply and efficiency based on the animal s form, structure and control theory becomes an important development trend. 2) Light weight and high payload: high power density drive device The drive device with high power density, light weight and high payload is the common key technology in the research area of robotics. Moreover, it is a prerequisite and core technology needed to break through for realizing the high dynamic, high adaptability and high payload capacity of bionic quadruped robots. 3) High mobility: fast response, high-speed locomotion and adaptation to the environment The new level and inevitable development trend of quadruped robots is to complete working tasks with high quality in the complex environments. The performance of fast response and high speed locomotion is a basic condition to deal with the impact of disturbance of environments and changing terrains, especially for complex tasks in field environments. Fast walking ability is also a research hotspot and an important task must be resolved for researching high performance quadruped robots. 4) Intelligence: learning, evolution and control automatically The mimicry of humans and biology capable of learning, evolution and decision-making control is very important to robot intelligence. It is a prerequisite of robots to accommodate the complex environments, complete working tasks and implement self learning and self evolution. Therefore, it is a significant developing direction and core content for the current and future robot research. 5) Man-machine harmonious: man-machine interaction and security coordination The basic criteria of robotics are to service and subjected to mankind, and keep harmonious between man and machine. The development of man-machine interaction technologies in terms of auditory, vision, gesture, brain s thinking and other multi-mode perception naturally and friendly is a basic task in the research of robotics. The purpose of man-machine harmony is to realize the man-machine interaction and security coordination in the future. IV. TECHNICAL DIFFICULTIES OF QUADRUPED ROBOTS A. Mechanical design of robots based on the form and structural bionics The first technical difficulty in designing quadruped robots is the construction of bionic mechanism. Biological data has been used to aid selection of the basic robot physical parameters, such as body length, leg stiffness and hip height. The influence of robot physical parameters on key quantities of robot performance, such as actuator effort and payload capability, has not been fully explored [26]. Based on the research of bionics and bionic technology of four legged animals, the mechanisms of bionic structure, different gait generation approaches and methods of restoring balance of body in some emergency situations are urgently needed to be investigated. The researchers can design the drive mechanism and ontology structure for quadruped robots with ingenious, large rigidity, light weight and flexible movement properties in accord with the modern bionics if this difficulty is resolved. Thus, the technical difficulty is to optimize the locomotion mechanism and further accomplish the design of structure with characteristics of lightweight, impact resistance, powerful obstacle negotiation and good stability. B. Design and manufacturing technology for the integrated hydraulic drive unit with characteristics of high bandwidth, small size and high accuracy 1) The design and manufacturing technology for the hydraulic drive which are united by integrated hydraulic cylinder, servo valve, force/position sensors and digital controller with characteristics of high pressure, high bandwidth, high precision, large flow and light weight is a technical difficulty. 2) The force-position hybrid control technology with characteristics of high-speed and high-precision is another technical difficulty. Hydraulic servo unit is a system with strong non-linear and strong uncertainty characteristics. The time-varying parameters and the variation of load force, speed and position have great impact on controlling hydraulic pressure of drive system. Therefore, the special hybrid control algorithm is needed to solve this problem. C. Environmental perception and autonomous navigation The key problems of realizing environmental perception and autonomous navigation in robotics are summarized as follows: heterogeneous source and multi-scale data registration, calibration and integration problems, semantic expression of object, environment and event design of artificial cognitive system based on intelligence biological cognitive mechanism, self alignment integrated navigation algorithms of long time and high precision, passable path planning of complex terrains, etc. D. Transient compliant generation technology of dynamic gaits of bionic quadruped robots Under the unstructured circumstances, various kinds of adaptive gaits should be taken for bionic quadruped robots. The transient requirement of gait transition is necessary for high maneuverability. The gait changing stability of posture transition and locomotion is required for locomotion stability. Meanwhile, the gait generation methods and locomotion control technologies are difficult to satisfy the requirements mentioned above because of the influences of inertial force, impulsive force, impact between foot and ground, interference of external force, sliding friction and other factors of gaits IEEE 5th International Conference on Robotics, Automation and Mechatronics (RAM) 169

5 E. The gait planning and dynamic locomotion control strategies for quadruped robots in condition of rapid movement, disturbance from ground and impact from external force, etc The quadruped robot is a serial parallel and highly branched-chain system. The parameters of the robot have large time-varying property. The effects of some complicated factors, such as large time varying of parameters, statically unstable property for dynamic gaits and instability in the changing terrains and impact from external force, bring the research of posture control strategy of stability many serious difficulties. F. The real-time locomotion and rapid perception technologies for complex terrains based on environmental perception One of the main developing goals of bionic quadruped robots is to realize stability and fast locomotion. Based on the pattern of environmental perception-modeling-reconstruction and the control of robot posture stability, target recognition, locomotion planning, gait planning and locomotion control subjected to dynamic constraints and other technology problems should be mainly solved and tracked. The real time adjusting of posture, gait, path and energy consumption problems should also be considered. The final goal is to realize the optimization of stability, mobility and energy consumption and completion of given tasks in the complex environments. G. The system integration method of quadruped robots with characteristics of high dynamic nature, high mobility and high payload capability The bionic quadruped robot with high performance is a highly level integrated platform covered a new bionic mechanism, micro and small power, density driver of high frequency and high power, high-speed dynamic environments, posture perception and high speed real time control. The complex integrated technologies of digital hydraulic servo, engine, sensors and electrical control system are needed for integration of the platform of quadruped robot. V. THE QUADRUPED ROBOT DEVELOPING BY SUCRO In the development of hydraulic drive quadruped robots, it is very important to design the driver actuators and to characterize the dynamic gaits. In 2010, an integrated hydraulic drive unit system designed for the quadruped being developed in SUCRO (Shandong University Center for Robotics) and Nanjing Engineering Institute of Aircraft Systems depicted in Fig. 2 and Fig. 3. The space borne special devices with high accuracy, large bandwidth and small characteristic are selected for constructing the servo valve, displacement sensor and pressure sensor. The cylinder and servo valve plate are integrated together for decreasing the weight of the hydraulic drive unit system. The strength check and modal analysis of the hydraulic drive unit system are simulated by ANSYS. The control performance and the optimization of the control parameters are evaluated by the semi-physical simulation system-dspace. The performance of the hydraulic drive unit system are as follows: the weight is less than 2kg, the maximum working stroke of the servo actuator is at most 60mm, the maximum dynamic force is 700kgf, the maximum working speed is 0.48m/s and the frequency of the servo actuator is much more than 100Hz. The performance of designed hydraulic drive unit system is enough for the quadruped robots with dynamic gaits and high power actuators to carry a considerable payload. Fig. 2. Scheme of the real hydraulic drive unit system. 1. Piston rod 2. Cylinder 3. Displacement sensor 4, 6. Prssure sensor 5, 7. Servo valve Fig. 3. CAD model of the integrated hydraulic drive unit. Based on above hydraulic actuators, an experimental platform of quadruped robot has been developed in SUCRO, which is called Hanma (SUCRO Hanma). The hydraulic drive quadruped robot we developed is shown in Fig. 4. The majority of the mechanical structure of the quadruped robot is constructed by an aluminum alloy due to its excellent strength to weight ratio. Its height is 0.67 m in initial posture. It is 1 m long and 0.4 m wide. Its weight is 50 kg not including hydraulic power source. Linear hydraulic actuators are installed for the quadruped robot to carry heavy payload and move fast on uneven terrain. One leg module comprises one hip joint, one shoulder joint and one knee joint, so the hydraulic quadruped has 12 degrees of freedom, with three degrees of freedom per leg. Fig. 4. The real model of the quadruped robot IEEE 5th International Conference on Robotics, Automation and Mechatronics (RAM)

6 We have done experiments with the platform of quadruped robot in the indoor environment and the walking speed is at least 1m/s with the trotting gait. Fig. 5 shows that the quadruped robot can move with 80-kg payload in a speed of 0.4m/s. The results of the experiments show that the developing robot platform has sufficient joint actuating power and rigidity. Fig. 5. The quadruped robot with 80 kg payload (0.4 m/s). VI. SUMMARY AND FUTURE WORK Quadruped robots demonstrate great mobility on different terrains and at different speed and gaits. In view of amazing and superior performance of BigDog robot and cheetah robot in the Boston Dynamics, a research boom of hydraulic quadruped robots has aroused in the robotics field. The realization of dynamic stability and airborne hydraulic actuator systems is the development trend and technical difficulty for bionic quadruped robots. Over the last five decades, quadruped robots have become faster, more efficient, more robust, and have a considerable payload capability. With the development of robotics, the intelligence bionic quadruped robots of adaptive ability of field environments with highly dynamics, fast speed and more payload capability will be constructed in the recent future. Compared with foreign advanced technology, the robotics of China is relatively backward and need to carry out relative research as soon as possible. We should make some breakthroughs in some common key techniques in order to promote the fast development of robotics and satisfy various requirements including national defense construction and others in China. REFERENCES [1] J. Z. Kolter, M. P. Rodgers and A.Y. Ng, A control architecture for quadruped locomotion over rough terrai, IEEE International Conference on Robotics and Automation, Pasadena, 2008, pp [2] M. H. Raibert, Legged robots, Communications of the ACM, vol. 29, no. 6, pp , [3] D. J. Todd, Walking machines: an introduction to legged robots. London: Kogan Page, pp [4] S. M. Song and K. J. Waldron, Machine That Walk-The Adaptive Suspension Vehicle. The MIT Press, 1989, pp [5] P. Gonzalez-de Santos, E. Garcia and J. Estremera, Quadrupedal Locomaotion: An Introduction to the Control of Four-legged Robot. London: Springer-Verlag, 2006, pp [6] M. H. Raibert, legged Robot That Balance. The MIT Press, 1986, ch. 4. [7] H. Kimura, I. Shimoyama and H. Miura, Dynamics in the dynamic walk of a quadruped robot, Advanced Robotics, vol. 4, no. 3, pp , [8] K. Yoneda and S. Hirose, Dynamic and static fusion gait of a quadruped walking vehicle on a winding path, IEEE International Conference on Robotics and Automation. 1992, vol. 1, pp [9] K. Berns, W. Ilg, M. Deck, J. Albiez and R. 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D. dissertation, Italian Institute of Technology and University of Genoa, [21] D. Q. He, Y. C. Liu, P. S. Ma, Research on influence of joint reactions on stability of quadruped machine walking in trot gait, proceedings of the Intelligent Control and Automation, 2008 WCICA th World Congress on, Chongqing, 2008, pp [22] X. L. Zhang, H. J. Zheng, L. F. Chen, Gait transition for a quadrupedal robot by replacing the gait matrix of a central pattern generator model, Advanced Robotics, vol. 20, no. 7, pp , [23] Y. Sun, X. D. Chen, T. H.Yan, W. C. Jia, Modules Design of a Reconfigurable Multi-Legged Walking Robot, In Proc. IEEE International Conference on Robotics and Biomimetics, Kunming, 2006, pp [24] X. D. Chen, Y. Sun and W. C. Jia, Motion Planning and Control of Multilegged Walking Robots. Wuhan, China: HUST Press, [25] C. Semini, N. G. Tsagarakis, E. Guglielmino and D. G. Caldwell, Design and experimental evaluation of the hydraulically actuated prototype leg of the HyQ robot, The 2010 IEEE/RSJ International confercence on Intelligent Robot and Systems, Taipei, Taiwan, 2010, pp [26] P. Chatazkos and E. Papadopoulos, Bio-inspired design of electrically-driven bounding quadrupeds via parametric analysis, Mechanism and Machine Theory, vol. 44, no. 3, pp , IEEE 5th International Conference on Robotics, Automation and Mechatronics (RAM) 171

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