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Designing a Quadruped Robot by Mimicking an Animal 1

Zhang Xiuli 2 Zheng Haojun 1 Zhao Guangtao 1 Guan Xu 1

1 Department of Precision Instruments and Mechanology, Tsinghua University,Beijing 100084, China

2 Department of Precision Mechanical Engineering, Shanghai University,Shanghai 200072, China

Abstract. The paper explored a way to design mechanical structure and motionpattern of a quadruped robot to realize pitching motion by mimicking amammal. Four joints configuration styles were acquired by simplifyinganimals body. Referring to the leg-motion-pattern of a cat, joint motiontrajectories were designed and motion relationship between knee and hip wasformulated for the quadruped robot. Proved by the simulations and theexperiments, all designs were effective and the quadruped robot could walk quickly, naturally and smoothly just like an animal. Otherwise, we foundrobotic mechanical structure in terms of joint-configuration style, layout of COG, etc. had influence on the performances of the robot. That could result inslippage or not-clearance-from-ground of feet in motion.

Key words: quadruped robot, biomimic, joint configuration, motion trajectory,structure design

Designing a legged robot was a tough task because there were complex nonlineardynamics involved in the multi-rigid-bodies system of a legged robot with redundantdegrees of freedom (DOF). It was very difficult to coordinate so many DOFs toachieve a smooth movement. It was a shortcut to design the structure and motiontrajectories of a legged robot by mimicking its counterparts in animal kingdom. Therewere many successful examples such as a robotic fish, robotic lobster, robotic snake,robotic insect, etc. But it was seldom to design a legged robot by mimicking ananimal from both its body and motion. It was worth to explore in this field. This paperintroduced a quadruped robot whose mechanical structure and joint motion trajectorywas designed by mimicking a cat. Section 1 presented the structure designing of thequadruped robot. Animals body could be simplified as four kinds of jointsconfigurations. Section 2 presented the motion trajectory designing by mimicking

1 Funded by the China National 863 Hi-Tech Program (No. 2001AA422330) and the National Natural ScienceFoundation of China.

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animals motion pattern. A mapping function from hip to knee was formulated.Section 3 presented the simulation and experimental results by employing the abovedesigns. Section 4 delivered our conclusions.

1 Designing the structure of a quadruped robot by mimicking

animals body

A leg of a quadruped mammal had five segments, which compose five joints byconnecting with trunk. Each joint had 1 to 3 DOFs. Owing to the super-redundantfreedoms, the motion of animal was very flexible. There were two sorts of joint inanimals, knee-style joint and elbow-style joint. Knee-style joint was one whose anglepoint was equidirectional to the pitch, for example, knee in a human. Elbow-style

joint was one whose angle point was opposite to the pitch, such as the elbow and theankle in a human. Generally, knee-style joint and elbow-style joint lay alternately inone leg, so that the leg could move up and down like a scissor. The jointsconfiguration of front and hind legs was of mirror image. The corresponding jointsbend oppositely, and they belong to knee-style joint or elbow-style joint (see Fig. 1) respectively. The joint-configuration style of animal was advantageous and efficientto motion.

Fig. 1 Body structure of a quadruped mammal (left: hind leg, right: front leg, threephases shown in the figure)

It was impossible to design the structure of a robot like an animal with 5-segmented legs and super-redundant freedoms, or controlling the robot would becomemuch too complicated (such as Ilg Ws Bisam [ 1]). So it must be reasonablysimplified of animals body when used in robot. According to Fig. 1 , Animals jointconfiguration could be simplified as four kinds (see Fig. 2 ):

a) All joints in front and hind legs were knee-style joints (Tsujita [ 2]);b) All were elbow-style joints (Kimuras Tekken [ 3]);c) Mirror image with front legs in knee-style and hind legs in elbow-style. We

named it outward-pointing configuration;

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d) Mirror image but reverse to c) with front legs in elbow-style joint and hind legsin knee-style joint (Sonys Aibo). We named it inward-pointing configuration.

(a) all-elbow configuration (b) all-knee configuration

(c) outward-pointing configuration (d) inward-pointing configuration

Fig. 2 Simplified joint-configuration styles of a mammal

According to the above principles, we designed the quadruped robot, Biosbot,which need complete pitching motion. Each leg of Biosbot had 3 joints of hip, kneeand ankle. Each joint had 1 DOF of pitch. The robot had 12 DOFs in all. The hip andknee were active joints. The passive joints of ankle were added in order to enhancethe adaptability to terrain. All joints could revolve up to around 180 degree. Biosbotcould form four different structures corresponding to Fig. 2 (see Fig. 3 ). The size of the robot was 400mm320mm300mm.

a) all-elbow configuration b) all-knee configuration

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c) outward-pointing configuration d) inward-pointing configuration

Fig. 3 The quadruped robot Biosbot in four different joint configurations

2 Designing the joint motion trajectories of the robot by

formulating a cats motion

The joint motion trajectories had very important effects on the performance of alegged robot, which determine whether or not the motion was steady and coordinated.

Traditionally, the joints trajectories of a legged robot were got by inverse kinematics;that was, planning foot placements then inverse-calculating the angles of all joints.That method was complex and slow in calculating a dynamic equation. And it wasalso difficult to obtain a smooth and suitable trajectory. On the contrary, the jointsmotion pattern of a mammal was so natural and elegant. It could be good referencefor a robot.

We conducted the research on the motion of a one-year-old cat by using a camera.Analyzing the motion videos, we found there was a specific relationship betweencats knee and hip when moving. The knee and the hip in the same leg movesynchronously during swing phase. Knee flexes in the prophase of the swing andreaches maximum position in the middle, while it extends in the anaphase of theswing and reaches to its original position at end. During stance phase, the hip swingsbackward and knee keeps motionless (see Fig. 4 ). Such a relationship between hipand knee had been observed in [ 4]. So it could be a common regularity in quadrupedmammals. Such motion relationship of hips and knees could ensure that feet of swinglegs always clear ground, and dont interfere with the motion of stance legs.

1 2 3 4

5 6 7 8

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9 10 11 12

13 14 15 16

17 18

Fig. 4 The motion of a cat (one period, the lines in the right front leg of the catindicates the position of its hip and knee)

Referring to the motion pattern of a mammal, we formulated the relationshipbetween the mammals hip and knee as . That was, the motion trajectory of knee jointwas obtained by inversing and translating the motion curve of hip joint in the sameleg. In order to avoid rubbing and stumbling at phase switch (stance to swing),alterable gain, k in , was introduced to perfect knee joint curve to produce higherspeed at beginning and at end. To knee-style joint and elbow-style joint, knee jointsand hip joints had different relation of revolution. So we added a sign flag, sgn( ), to the function, which acquired different value according to the joint style. The positionfunction of knee joint was defined as follows:

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0

0

sgn( )( ( ) ) ( ), ( 0, swing phase),( )

0, ( 0, stance phase),

( )( ) (1 ),

/ ,

1, (kneeflag of joint style:

1, (elbow

( / ).

h h h

k

h

h

h

k h

A t k t t

t k t k

A

k A A

d dt

=