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Computer Research and Modeling, 2020, Volume 12, Issue 1, Pages 155–170
DOI: https://doi.org/10.20537/2076-7633-2020-12-1-155-170
(Mi crm777)
 

MODELS IN PHYSICS AND TECHNOLOGY

Searching for realizable energy-efficient gaits of planar five-link biped with a point contact

R. R. Khusainov, Sh. N. Mamedov, S. I. Savin, A. S. Klimchik

Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 1 University st., Innopolis, 420500, Russia
References:
Abstract: In this paper, we discuss the procedure for finding nominal trajectories of the planar five-link bipedal robot with point contact. To this end we use a virtual constraints method that transforms robot's dynamics to a low-dimensional zero manifold; we also use a nonlinear optimization algorithms to find virtual constraints parameters that minimize robot's cost of transportation. We analyzed the effect of the degree of Bezier polynomials that approximate the virtual constraints and continuity of the torques on the cost of transportation. Based on numerical results we found that it is sufficient to consider polynomials with degrees between five and six, as further increase in the degree of polynomial results in increased computation time while it does not guarantee reduction of the cost of transportation. Moreover, it was shown that introduction of torque continuity constraints does not lead to significant increase of the objective function and makes the gait more implementable on a real robot. We propose a two step procedure for finding minimum of the considered optimization problem with objective function in the form of cost of transportation and with high number of constraints. During the first step we solve a feasibility problem: remove cost function (set it to zero) and search for feasible solution in the parameter space. During the second step we introduce the objective function and use the solution found in the first step as initial guess. For the first step we put forward an algorithm for finding initial guess that considerably reduced optimization time of the first step (down to 3–4 seconds) compared to random initialization. Comparison of the objective function of the solutions found during the first and second steps showed that on average during the second step objective function was reduced two fold, even though overall computation time increased significantly.
Keywords: bipedal robot, underactuated system, hybrid system, optimal trajectory.
Funding agency Grant number
Russian Foundation for Basic Research 18-38-00945
This work was supported by RFBR grant No. 18-38-00945.
Received: 13.01.2020
Accepted: 16.01.2020
Document Type: Article
UDC: 004.896: 621.865
Language: Russian
Citation: R. R. Khusainov, Sh. N. Mamedov, S. I. Savin, A. S. Klimchik, “Searching for realizable energy-efficient gaits of planar five-link biped with a point contact”, Computer Research and Modeling, 12:1 (2020), 155–170
Citation in format AMSBIB
\Bibitem{KhuMamSav20}
\by R.~R.~Khusainov, Sh.~N.~Mamedov, S.~I.~Savin, A.~S.~Klimchik
\paper Searching for realizable energy-efficient gaits of planar five-link biped with a point contact
\jour Computer Research and Modeling
\yr 2020
\vol 12
\issue 1
\pages 155--170
\mathnet{http://mi.mathnet.ru/crm777}
\crossref{https://doi.org/10.20537/2076-7633-2020-12-1-155-170}
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