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Analysis of double support phase of biped robot and multi-objective optimization using genetic algorithm and particle swarm optimization algorithm

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Abstract

This paper deals with multi-objective optimization in gait planning of a 7-dof biped robot during its double support phase, while ascending and descending some staircases. For determining dynamic balance margin of the robot in terms of zero-moment point, its double support phase has been assumed to be consisting of two single support phases on non-coincidental parallel surfaces. Thus, dynamic balance margin of the biped robot during its double support phase is obtained by using a virtual zero-moment point of the system. Moreover, a smooth transition from single to double support phases in a cycle is to be maintained for the walking robots. Two contrasting objectives, namely power consumption and dynamic balance margin have been considered during optimization. Pareto-optimal fronts of solutions are obtained using genetic algorithm and particle swarm optimization algorithm, separately. To the best of the authors’ knowledge, it is the first attempt to solve multi-objective optimization problem in double support phase of a biped robot.

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Acknowledgements

The authors thank All India Council of Technical Education (AICTE), Govt. of India, for supporting this study and Mr. Ashutosh Kumar Misra, for providing some useful suggestions.

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Authors and Affiliations

  1. Soft Computing Laboratory, Mechanical Engineering Department, Indian Institute of Technology, Kharagpur, Kharagpur, 721 302, India

    REGA RAJENDRA & DILIP KUMAR PRATIHAR

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  1. REGA RAJENDRA
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  2. DILIP KUMAR PRATIHAR
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Correspondence to DILIP KUMAR PRATIHAR.

Appendix A

Appendix A

1.1 Expressions for Joint Torques

The equations of n joint torques can be written as follows (Fu et al 1987):

$$ \tau_{i} =\sum\limits_{k=1}^{n} {D_{ik} } \ddot{{q}}_{k} +\sum\limits_{k=1}^{n} {\sum\limits_{m=1}^{n} {h_{ikm} \dot{{q}}_{k} } } \dot{{q}}_{m} +C_{i} , \mathrm{i}=1, 2. . . , \mathrm{n}, $$
(A1)
$$ D_{ik} =\sum\limits_{j=\max (i,k)}^{n} {Tr(U_{jk} J_{j} U_{ji}^{T} } ),\quad \mathrm{i}, \mathrm{k} = 1, 2,. . . , \mathrm{n}, $$
(A2)
$$ h_{ikm} =\sum\limits_{j=\max (i,k,m)}^{n} {Tr({U_{jkm} J_{j} U_{ji}^{T} } )} ,\mathrm{i}, \mathrm{k}, \mathrm{m} = 1, 2. . ., \mathrm{n}, $$
(A3)
$$ C_{i} =\sum\limits_{j=1}^{n} {({-m_{j} gU_{ji} {\overline{r}_{j}^{j}} } )} , \mathrm{i} =1, 2. . ., \mathrm{n}, $$
(A4)

where D i k denotes inertia terms, h i k m represents the Coriolis and centrifugal terms, and C i indicates information of the gravity terms.

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RAJENDRA, R., PRATIHAR, D.K. Analysis of double support phase of biped robot and multi-objective optimization using genetic algorithm and particle swarm optimization algorithm. Sadhana 40, 549–575 (2015). https://doi.org/10.1007/s12046-014-0327-5

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  • DOI: https://doi.org/10.1007/s12046-014-0327-5

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