Improved forward kinematic analysis of a reptile-like four-legged walking robot using a novel dimensionality-reduction method

Abstract

A new forward kinematic analysis is proposed to describe the motion of a reptile-like four-legged walking robot using a new dimensionality-reduction method. The three standing legs (assuming one leg is swinging) contain nine driven joints. Only six of these joints, however, are independently driven joints. The remaining joints are redundant driven joints. Finding the redundant driven joint angles has been a key problem in improved forward kinematic analysis of a reptile-like forward kinematic analysis. Solving the associated high-order equation, which is derived using the analytic method, is problematic and slow. In this paper, we use a new dimensionality reduction method to solve this problem. First, we deduced the formulas for the redundant driven joint angles. Then, one of the formulas is transformed to take into account the constraint condition. We then use iteration to find solutions for the remaining equations that satisfy the constraint condition. With the help of MATLAB, a solving system for the forward kinematic analysis of this robot is introduced. Our results show two improvements over the conventional method: shorter computation time and higher precision.

Keywords

Four-legged walking robots reptile-like kinematics analytic method dimensionality-reduction method

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References

Buchli

Pratt

Roy

. Editorial: special issue on legged locomotion. Int J Robot Res 2011; 30: 139–140.

Raibert M, Blankespoor K, Nelson G, et al. Bigdog, the rough-terrain quadruped robot. In: Jin MC and Pradeep M (eds) Processing of the 17th world congress of the international federation of automatic control, Seoul, Korea, 2008, pp.10822–10825. COEX, Korea, South: World Congress, Volume # 17|Part# 1.

Wang

Chen

Wang

. Motion error compensation of multi-legged walking robots. Chin J Mech Eng 2012; 25: 639–646.

Berns

Ilg

Deck

. Mechanical construction and computer architecture of the four-legged walking machine BISAM. IEEE/ASME Trans Mech 1999; 4: 32–38.

Hirose S and Kato K. Study on quadruped walking robot in Tokyo institute of technology-past, present and future. In: Processing of the 2000 IEEE international conference on robotics and automation (ICRA 2000), 2000, pp.414–419. San Francisco, CA: IEEE.

Wang

Chen

. A study of analytical forward kinematics of multi-legged walking robot locomotion. Mach Intell Robot Contr 2004; 6: 29–37.

Gallardo-Alvarado

. Enhancing the originality of the Stewart platform through its kinematic analyses. Proc IMechE, Part C: J Mech Eng Sci 2012; 226: 3013–3025.

Angeles

. Fundamentals of robotic mechanical systems: theory, methods, and algorithms, Montreal, QC, Canada: Springer International Publishing, 2002.

Shi ZM and Gan DY. Kinematics of six-legged vehicles on irregular terrain. In: Processing of international conference on advanced robotics, Tokyo, Japan, 1985, pp.389–396. Beijing, China: Science Publishers.

10.

Chen X D, Watanabe K and Izumi K. Kinematic solution of a quadruped walking robot-posture analysis of TITAN-VIII. In: Processing of 14th IFAC world congress, 1999, pp.343–348. Oxford, England: Pergamon Press.

11.

Nokleby

Fisher

Podhorodeski

. Force capabilities of redundantly-actuated parallel manipulators. Mech Mach Theory 2005; 40: 578–599.

12.

Boudreau

Turkkan

. Solving the forward kinematics of parallel manipulators with a genetic algorithm. J Robot Syst 1996; 13: 111–125.

13.

Didrit

Petitot

Walter

. Guaranteed solution of direct kinematic problems for general configurations of parallel manipulators. IEEE Trans Robot Autom 1998; 14: 259–266.

14.

Innocenti

Parenti-Castelli

. Direct position analysis of Stewart platform mechanism. Mech Mach Theory 1990; 25: 611–621.

15.

Kim

Park

. Direct kinematic analysis of 3-RS parallel mechanisms. Mech Mach Theory 2001; 36: 1121–1134.

16.

Song

Kwon

. Efficient formulation approach for the forward kinematics of 3-6 parallel mechanisms. Adv Robot 2002; 16: 191–215.

17.

Etemadi-Zanganeh

Angeles

. Real-time direct kinematics of general six-degree-of-freedom parallel manipulators with minimum-sensor data. J Robot Syst 1995; 12: 833–844.

18.

Han K, Chung WK and Youm Y. Local structurization for the forward kinematics of parallel manipulators using extra sensor data. In: Processing of IEEE international conference on robotics and automation, Nagoya, Aichi, Japan, 1995, pp.514–520. New York: IEEE.

19.

Bonev

Ryu

. A new method for solving the direct kinematics of general 6-6 Stewart platform using three linear extra sensors. Mech Mach Theory 2000; 35: 423–436.

20.

MATLAB, http://www.mathworks.cn/products/matlab/ (accessed 22 August 2012).

21.

Wang

. A geometric approach to solving the stable workspace of quadruped bionic robot with hand–foot-integrated function. Robot Comput Integr Manuf 2016; 37: 68–78.