Patent ID: 11926063
Assignee: YANSHAN UNIVERSITY
Field: Handling (Mechanical engineering)
Classification: CPC B  G | IPC B

Claim 2:
3. The method according to claim 1, characterized in that, the position tracking errors of the master robot and the slave robot in step S3 are:

em=qm−qs(t−ds)

es=qs−qm(t−dm)  (7)

in which, em represents position tracking error of the master robot; es represents position tracking error of the slave robot; dm represents fixed-length time delay of forward information transmission from the master robot to the slave robot; ds represents fixed-length time delay of backward information transmission from the slave robot to the master robot, and dm≠ds; t represents an operating time;
the fractional order nonsingular rapid terminal sliding mode surface equation is:

sm(t)=ėm+αm1Dα1−1[sig(em)γm1]+αm2Dα2[βm(em)]

ss(t)=ės+αs1Dα1−1[sig(es)γs1]+αs2Dα2[βs(es)]  (8)

in which, si represents designed fractional order nonsingular fast terminal sliding mode surface, si=[si1, si2, . . . sin]T∈Rn; γi1 is a positive constant, γm1,γs1>1; α1, α2 represent fractional orders and α1∈(0,1],α2∈[0,1); Dαi−1sig(ei)γi1] represents α1−1 ordered Riemann-Liouville fractional order derivative of sig(ei)γi1; Dα2[βi(ei)] represents α2 ordered Riemann-Liouville fractional order derivative of βi(e1); αi1 and αi2 both represent parameters of the sliding mode surface equation and are positive definite diagonal matrix, αi1=diag(αi11, αi12, . . . , αi1n), αi2=diag(αi21, αi22, . . . , αi2n); functions βm(em), βs(es) are described as:, β
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in which, sm represents a terminal sliding mode surface which shows that the main robot has a singularity problem, sm=ėm+αm1Dα1−1[sig(em)γm1]+αm2Dα2[sig(em)γm2]; ss represents a terminal sliding mode surface which shows that the slave robot has a singularity problem, ss=ės+αs1Dα1−1[sig(es)γs1]+αs2Dα2[sig(es)γs2]; γi2 is a positive constant, 0<γm2,γs2<1; km1 is a positive constant, km1=(2−γm2)δmγm2−1; km2 is a positive constant, km2=(γm2−1)δmγm2−2; ks1 is a positive constant, ks1=(2−γs2)δsγm2−1; ks2 is a positive constant, ks2=(γs2−1)δsγs2−2; δm,δs represents designed small constant.