Abstract
A compact dynamic model and a hybrid position/force controller for a constrained robot manipulator, subject to a set of holonomic (integrable) constraints have been developed in this study. The joint-space dynamics (DAEs) has been transformed into the constraint-space model in which the system dynamics can be readily decomposed into two orthogonal subsystems; the motion-controlled subsystem is specified in the direction tangential to the known constraint surfaces, and the force-controlled subsystem is regulated in the orthogonal direction. Also utilizing the transformed dynamics, we have presented a hybrid adaptive control law to simultaneously manipulate the end-effector position and the contact force. Further, by a Lyapunov theory, it has been shown that the corresponding closed-loop system is globally stable under the parametric uncertainties.
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Abbreviations
- ℜ+ :
-
A set of non-negative real number; ℜ+ : = [0, + ∞)
- ℜn :
-
Then-dimensional vector space with real elements ℜ
- ℜx ×m :
-
A set of all real-valued(n×m) matrices
- sup :
-
The supremum, the least upper bound
- ‖x‖:
-
The Euclidean norm of a vectorx; ‖x‖ = [x T x]1/2, ∀x∈ℜn
- A >0(<0):
-
A positive(negative) definite matrixA
- λ max (A):
-
The maximum eigenvalue of matrixA:\(A ; \lambda _{max} \left( A \right) = \mathop {\max }\limits_i \left\{ {\lambda _i \left( A \right)} \right\}\), whereλ i (A) is thei the eigenvalue of matrixA
- λ min (A):
-
The minimum eigenvalue of matrixA;\(A ; \lambda _{min} \left( A \right) = \mathop {\min }\limits_i \left\{ {\lambda _i \left( A \right)} \right\}\)
- ‖A‖:
-
The induced norm of a real matrixA ∈ ℜn ×m ; ‖A‖ = [λ max (A T A)]1/2
- C p :
-
A set ofp-times continuously differentiable functions
- E nxn :
-
An (nxn) identity matrix
- 0 n :
-
An-dimensional null vector
- 0 nn :
-
A (nxn) null matrices
- L p :
-
The function norm in the Lebesgue space; Letf(t) : ℜ+ → ℜn be Lebesgue measurable function, then theL p -norm ‖f‖ p is defined as ‖f‖ p = [∫0 ∞ ‖f(t)‖p dt]1/p < 0 forp∈[1, ∞). Whenp=∞,f∈L ∞ if and only if\(\left\| f \right\|_\infty = \mathop {sup}\limits_{t \in [0, + \infty )} \left\| {f\left( t \right)} \right\|< \infty \)
- (O)c :
-
A complement of (O)
- rs(A) :
-
The range space of matrixA(or column space ofA)
- rk(A) :
-
The rank of matrixA
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You, S.S. A unified dynamic model and control synthesis for robotic manipulators with geometric end-effector constraints. KSME Journal 10, 203–212 (1996). https://doi.org/10.1007/BF02953659
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DOI: https://doi.org/10.1007/BF02953659