Minimum-time pointing control of a two-link manipulator

Wie, Bong; Chuang, Ching-Te; Sunkel, John W.

doi:10.2514/6.1988-4117

Cited by 4 publications

(9 citation statements)

References 7 publications

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“…where X 0 6 with X 6 .t I / D 0 is the multiplier associated with the differential constraint (32), X 0 7 with X 7 .t I / D 0 is the multiplier associated with the differential constraint (33), and X 0 8 with X 8 .t I / D 0 and X 0 9 with X 9 .t I / D 0 are the multipliers associated with the additional differential constraints (31). Variable X 0 10 with X 10 .t I / D 0 is the multiplier associated with the constraint Â 2 6 Â 2u , and X 0 11 with X 11 .t I / D 0 is the excess variable associated with the same constraint.…”

Section: Pendubotmentioning

confidence: 99%

“…Simple bound constraints To express this optimal control problem which involves second-order differential constraints in the form of a basic optimal control problem, we can proceed as explained in Section 8.1, introducing the change of variables (30) and the additional differential constraints (31). In this way, the second-order differential equations (41)and (42) are converted into first-order differential equations…”

Section: Acrobotmentioning

confidence: 99%

“…and relations (31), (44), and (45) are now the differential constraints of the optimal control problem. Then, we apply the Bliss multiplier rule, introducing the new variables (35), where X 1 , : : : , X 5 are defined in (36), X 0 6 with X 6 .t I / D 0 is the multiplier associated with differential constraint (44), X 0 7 with X 7 .t I / D 0 is the multiplier associated with the differential constraint (45), and X 0 8 with X 8 .t I / D 0 and X 0 9 with X 9 .t I / D 0 are the multipliers associated with the additional differential constraints (31). Variables X 10 , : : : , X 13 are the multiplier and the excess variables associated with the simple bound constraints (43), as explained in Section 8.1.…”

Section: Acrobotmentioning

confidence: 99%

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Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Gregory

Olivares

Staffetti

2012

Optim Control Appl Methods

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SUMMARYIn this paper, we study the trajectory-planning problem for planar underactuated robot manipulators with two revolute joints in the presence of gravity. This problem is studied as an optimal control problem. We consider both possible models of planar underactuated robot manipulators, namely with the elbow joint not actuated, called Pendubot, and with the shoulder joint not actuated, called Acrobot. Our method consists of a numerical resolution of a reformulation of the optimal control problem, as an unconstrained calculus of variations problem, in which the dynamic equations of the mechanical system are regarded as constraints and treated by means of special derivative multipliers. We solve the resulting calculus of variations problem by using a numerical approach based on the Euler-Lagrange necessary condition in integral form. In which, time is discretized, and admissible variations for each variable are approximated using a linear combination of the piecewise continuous basis functions of time. In this way, a general method for the solution of optimal control problems with constraints is obtained, which, in particular, can deal with nonintegrable differential constraints arising from the dynamic models of underactuated planar robot manipulators with two revolute joints in the presence of gravity.

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Section: Pendubotmentioning

confidence: 99%

Section: Acrobotmentioning

confidence: 99%

Section: Acrobotmentioning

confidence: 99%

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Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Gregory

Olivares

Staffetti

2012

Optim Control Appl Methods

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“…Most of the work in minimum-time trajectory planning has been for rigid, non-redundant, completely actuated manipulators, where non-redundant means the end effector path completely determines the path in joint space (to within a finite number of possibilities). Exemplary is the work of Bobrow [2] and Shin and McKay 113,12,16,141. Here, the trajectory of the system along this path can be completely specified using a single path parameter "s(t)." Bobrow [2] fmt constructed an infeasible region in input torques for keeping the system on the path are not available) and then utilized a trial and e m r procedure for finding switching curves in the state space.…”

Section: Introductionmentioning

confidence: 99%

“…Yet our algorithm is solving the above mentioned three link arm problem in times comparable to the solve times for much simpler problems solved with the Order(N) method of Wright [16], even though our problem is much more difficult because it is a highly nonlinear problem, with many active inequality constraints at the solution, typical of minimum time problems.…”

Section: Introductionmentioning

confidence: 99%

A Fast and Robust Algorithm for General Inequality/Equality Constrained Minimum-Time Problems

Driessen

Sadegh

Parker

et al. 1999

Journal of Dynamic Systems, Measurement, and Control

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the state space (s, S ) (regions for which the appropriate Abstract This paper presents a new algorithm for solving general inequalitylequality constrained minimum time problems. The algorithm's solution time is linear in the number of Runge-Kutta steps and the number of parameters used to discretize the control input history.The method is being applied to a thee link redundant robotic arm with torque bounds, joint angle bounds, and a specified tip path. It solves case after case within a graphical user interface in which the user chooses the initial joint angles and the tip path with a mouse. Solve times are h m 30 to 120 seconds on a hewlett packard workstation. A zero torque history is always used in the initial guess, and the algorithm has never crashed, indicating its robustness.The algorithm solves for a feasible solution for large trajectory execution time t, and then reduces t, by a small amount and re-solves. The futed time re-solve uses a new method of finding a near-minimum-2-norm solution to a set of linear equations and inequalities that achieves quadratic convergence to a feasible solution of the full nonlinear problem.On the other hand, our method, applied to the three-link-arm path constrained problem described in the Abstract and Section 3.2.8, solves case after case, each within 30 to 120 seconds, within a graphical user interface in which the user selects the tip path with a mouse, and the initial guess always has a zero torque history.An interesting contrast to the above methods was presented by Zimmerman and Layton [18]. To generate a This work * . ' United Con tract CE-ACn4 -94ALRWO. completed in part at Sandia National Laboratories, Albuquerque, NM States D v a der i

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Minimum-Energy Control of Two-Link Manipulator withPure State Constraints

Subchan¹

2005

LIMITS

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This paper presents an analysis and numerical solutions of the minimum-energy control of two-link robot manipulator. The minimum-energy control point-to-point trajectory is investigated subject to control constraints and state constraints on the angular velocities. The numerical solutions are solved by transforming the original problem into a nonlinear programming problem. The mathematical analysis of the optimal control problems is done based on the numerical results using an indirect method. The necessary conditions can be stated as a multi-point boundary value problems.

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Minimum-time pointing control of a two-link manipulator

Cited by 4 publications

References 7 publications

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

Energy‐optimal trajectory planning for the Pendubot and the Acrobot

A Fast and Robust Algorithm for General Inequality/Equality Constrained Minimum-Time Problems

Minimum-Energy Control of Two-Link Manipulator withPure State Constraints

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