Abstract
Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.
Highlights
Ôàçà îäíîîïîðíîãî äâèæåíèÿÏåðåìåùåíèå øàãàþùåãî äâóíîãîãî ðîáîòà ïî ëþáîé ïîâåðõíîñòè ïðåäñòàâëÿåò ñîáîé ïîñëåäîâàòåëüíóþ ñìåíó äâóõ ôàç | ôàçû îäíîîïîðíîãî äâèæåíèÿ è ôàçû ïåðåõîäà ðîáîòà ñ îäíîé íîãè íà äðóãóþ
Øàãàþùèå ìåõàíèçìû íàøëè øèðîêîå ïðèìåíåíèå â ñîâðåìåííîì ìèðå
Âïîñëåäñòâèè óêàçàííûé ïîäõîä áûë ïðèìåíåí äëÿ óïðàâëåíèÿ ïëîñêèì ïåðåìåùåíèåì ïÿòèçâåííîãî [12] è ñåìèçâåííîãî [13] øàãàþùèõ ìåõàíèçìîâ ïî ãîðèçîíòàëüíîé ïîâåðõíîñòè
Summary
Ïåðåìåùåíèå øàãàþùåãî äâóíîãîãî ðîáîòà ïî ëþáîé ïîâåðõíîñòè ïðåäñòàâëÿåò ñîáîé ïîñëåäîâàòåëüíóþ ñìåíó äâóõ ôàç | ôàçû îäíîîïîðíîãî äâèæåíèÿ è ôàçû ïåðåõîäà ðîáîòà ñ îäíîé íîãè íà äðóãóþ. Ïîëîæåíèå ïÿòèçâåííîãî ðîáîòà íà ôàçå îäíîîïîðíîãî äâèæåíèÿ îäíîçíà÷íî îïðåäåëÿåòñÿ ïÿòüþ îáîáùåííûìè óãëîâûìè êîîðäèíàòàìè q11, q31, q32, q41, q42  ðàáîòå [12] ïîêàçàíî, ÷òî ïîâåäåíèå ðîáîòà íà ôàçå îäíîîïîðíîãî äâèæåíèÿ îïèñûâàåòñÿ ñèñòåìîé îáûêíîâåííûõ äèôôåðåíöèàëüíûõ óðàâíåíèé. Ãäå q = (q11, q31, q32, q41, q42)ò, D(q) | ñèììåòðè÷íàÿ ïîëîæèòåëüíî îïðåäåëåííàÿ ìàòðèöà ïÿòîãî ïîðÿäêà ñ ýëåìåíòàìè. D11 = mtp2t + Jt, D12 = 0, D13 = −Lmtptc−, D14 = 0, D15 = −Lptmtc−, D22 = mbp2b + mgL2 + Jb, D23 = −L(mbpb + mgL)c32−31, D24 = Lpgmgc−, D25 = −(Lpbmb + mgL2), D33 = L2(mt + mb + mg) + mb(L − pb)2 + Jb, D34 = −mgLpgc−, D35 = (L2(mt + 2mb + mg) − mbLpb)c32−42, D44 = mgp2g + Jg, D45 = −mgLpgc−, D55 = L2(mg + 2mb + mt) + mg(L − pg)2 + Jg, C(q, q) | êâàäðàòíàÿ ìàòðèöà ïÿòîãî ïîðÿäêà ñ ýëåìåíòàìè.
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