Research Papers

Triple Stance Phase Displacement Analysis With Redundant and Nonredundant Sensing in a Novel Three-Legged Mobile Robot Using Parallel Kinematics

[+] Author and Article Information
Ping Ren

Department of Mechanical Engineering, Robotics & Mechanisms Laboratory (RoMeLa), Virginia Polytechnic Institute and State University, Blacksburg, VA 24061renping@vt.edu

Dennis Hong1

Department of Mechanical Engineering, Robotics & Mechanisms Laboratory (RoMeLa), Virginia Polytechnic Institute and State University, Blacksburg, VA 24061dhong@vt.edu

Please note that the arrangement of three rotator joints in Fig. 4 is slightly different from those in Fig. 1, where two rotator joints are aligned and the swing leg is ready to take a step (Fig. 2). The following sections use the configuration in Fig. 4 to elaborate the displacement analysis, without losing generality.


Corresponding author.

J. Mechanisms Robotics 1(4), 041001 (Sep 02, 2009) (11 pages) doi:10.1115/1.3204251 History: Received April 06, 2008; Revised April 10, 2009; Published September 02, 2009

This paper presents the forward and inverse displacement analysis of a novel three-legged walking robot Self-excited Tripedal Dynamic Experimental Robot (STriDER) in its triple stance phase. STriDER utilizes the concept of passive dynamic locomotion to walk, but when all three feet of the robot are on the ground, the kinematic configuration of the robot behaves like an in-parallel manipulator. To plan and control its change in posture, the kinematics of its forward and inverse displacement must be analyzed. First, the concept of this novel walking robot and its unique tripedal gait are discussed, followed by the overall kinematic configuration and definitions of its coordinate frames. When all three feet of the robot are on the ground, by assuming there is no slipping at the feet, each foot contact point is treated as a passive spherical joint. Kinematic analysis methods for in-parallel manipulators are briefly reviewed and adopted for the forward and inverse displacement analysis for this mobile robot. Both loop-closure equations based on geometric constraints and the intersection of the loci of the feet are utilized to solve the forward displacement problem. Analytical solutions are identified and discussed in the cases of redundant sensing with displacement information from nine, eight, and seven joint angle sensors. For the nonredundant sensing case using information from six joint angle sensors, it is shown that analytical solutions can only be obtained when the displacement information is available from unequally distributed joint angle sensors among the three legs. As for the case when joint angle sensors are equally distributed among the three legs, it will result in a 16th-order polynomial with respect to a single variable, and closed-form forward displacement solutions can be obtained. Finally, results from the simulations are presented for both inverse displacement analysis and the nonredundant sensing case with equally distributed joint angle sensors. It is found that at most 16 forward displacement solutions exist if displacement information from two joint angle sensors per leg are used and one is not used.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

STriDER (Self-excited Tripedal Dynamic Experimental Robot)

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Figure 2

Single step tripedal gait

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Figure 3

STriDER prototypes

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Figure 4

Coordinate frames and joint definitions

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Figure 5

Serial manipulator representation of a single leg

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Figure 6

Intersection of two circles [3-3-2 case]

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Figure 7

Sphere and circle intersection [3-3-1 case]

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Figure 8

Self-intersecting horn torus

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Figure 9

Torus and circle intersection [3-3-1 case]

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Figure 10

Planar ring and circle intersection [3-3-1 case]

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Figure 12

Forward displacement solution 1

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Figure 11

General nonredundant sensing [2-2-2 case]

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Figure 17

Forward displacement solution 6

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Figure 16

Forward displacement solution 5

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Figure 15

Forward displacement solution 4

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Figure 14

Forward displacement solution 3

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Figure 13

Forward displacement solution 2




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