Nonholonomic control of a three-DOF planar underactuated manipulator

Arai, Hirohiko; Tanie, K.; Shiroma, Naoji

doi:10.1109/70.720345

Cited by 198 publications

(97 citation statements)

References 29 publications

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“…A case study that obtained large attention is the planar 3R robot with the last passive joint. The so-called center of percussion 6 (CP) of the third (passive) link has been used for solving rest-to-rest motion problems in [1] and in [16]. In particular, in [1] the planning strategy consists of a sequence of translational and rotational (around the CP point) motions of the third link, while [16] use the fact that the CP position is a flat output for the system.…”

Section: A Planar Robot With Two Passive Jointsmentioning

confidence: 99%

“…The so-called center of percussion 6 (CP) of the third (passive) link has been used for solving rest-to-rest motion problems in [1] and in [16]. In particular, in [1] the planning strategy consists of a sequence of translational and rotational (around the CP point) motions of the third link, while [16] use the fact that the CP position is a flat output for the system. Thanks to partial feedback linearization (see (15)), this result applies whatever is the type of the first two actuated joints.…”

Section: A Planar Robot With Two Passive Jointsmentioning

confidence: 99%

“…Under a special hinging assumption, namely that each link has the following passive joint axis located at its center of percussion, it has been shown that the CP position of the last link is a flat output for the system [34]. The sequential planning algorithm of [1] has been extended in [45] to this case, while the flatness approach has been detailed in [22]. We summarize here the results of [22] for the case n = 4, characterizing also potential dynamic singularities that should be avoided at the planning stage.…”

Section: A Planar Robot With Two Passive Jointsmentioning

confidence: 99%

“…We just mention here the recently introduced kinematic reduction method for dynamic models of underactuated robots [9]. Based on the concept of kinematic controllability, it is possible in some cases to backup a dynamic motion planning problem into a sequence of elementary velocity commands along so-called decoupling vector fields (see, e.g., [1] for the application to a planar 3R robot with the last passive joint).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, even if some underactuated robots are known to be flat (see, e.g., [1,17]), a deeper analysis of specific planning solutions and of singularities are of interest in the dynamic case. This is the subject of the two other case studies presented later on.…”

Section: Introductionmentioning

confidence: 99%

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Planning Motions for Robotic Systems Subject to Differential Constraints

Luca

Oriolo

Vendittelli

et al. 2004

Springer Tracts in Advanced Robotics

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Abstract. We consider the problem of planning point-to-point motion for general robotic systems subject to non-integrable differential constraints. The constraints may be of first order (on velocities) or of second order (on accelerations). Various nonlinear control techniques, including nilpotent approximations, iterative steering, and dynamic feedback linearization, are illustrated with the aid of four case studies: the plate-ball manipulation system, the general two-trailer mobile robot, a two-link robot with flexible forearm, and a planar robot with two passive joints. The first two case studies are non-flat nonholonomic kinematic systems, while the last two are flat underactuated dynamic systems.

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Section: A Planar Robot With Two Passive Jointsmentioning

confidence: 99%

Section: A Planar Robot With Two Passive Jointsmentioning

confidence: 99%

Section: A Planar Robot With Two Passive Jointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Planning Motions for Robotic Systems Subject to Differential Constraints

Luca

Oriolo

Vendittelli

et al. 2004

Springer Tracts in Advanced Robotics

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Normal forms and internal regularization of nonlinear differential‐algebraic control systems

Chen

Trenn

Respondek

2021

Intl J Robust & Nonlinear

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In this article, we propose two normal forms for nonlinear differential‐algebraic control systems (DACSs) under external feedback equivalence, using a notion called maximal controlled invariant submanifold. The two normal forms simplify the system structures and facilitate understanding the various roles of variables for nonlinear DACSs. Moreover, we study when a given nonlinear DACS is internally regularizable, that is, when there exists a state feedback transforming the DACS into a differential‐algebraic equation (DAE) with internal regularity, the latter notion is closely related to the existence and uniqueness of solutions of DAEs. We also revise a commonly used method in DAE solution theory, called the geometric reduction method. We apply this method to DACSs and formulate it as an algorithm, which is used to construct maximal controlled invariant submanifolds and to find internal regularization feedbacks. Two examples of mechanical systems are used to illustrate the proposed normal forms and to show how to internally regularize DACSs.

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Feedback linearization of nonlinear differential‐algebraic control systems

Chen

Respondek²

2021

Intl J Robust & Nonlinear

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In this article, we study feedback linearization problems for nonlinear differential-algebraic control systems (DACSs). We consider two kinds of feedback equivalences, namely, external feedback equivalence, which is defined (locally) on the whole generalized state space, and internal feedback equivalence, which is defined on the locally maximal controlled invariant submanifold (i.e., on the set where solutions exist). We define a notion called explicitation with driving variables, which is a class of ordinary differential equation control systems (ODECSs) attaching to a given DACS. Then we give necessary and sufficient conditions for both internal and external feedback linearization problems of the DACS. We show that the feedback linearizability of the DACS is closely related to the involutivity of the linearizability distributions of the explicitation systems. Finally, we illustrate the results of the by an academic example and a constrained mechanical system.

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Nonholonomic control of a three-DOF planar underactuated manipulator

Cited by 198 publications

References 29 publications

Planning Motions for Robotic Systems Subject to Differential Constraints

Planning Motions for Robotic Systems Subject to Differential Constraints

Normal forms and internal regularization of nonlinear differential‐algebraic control systems

Feedback linearization of nonlinear differential‐algebraic control systems

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