Nearest optimal repeatable control strategies for kinematically redundant manipulators

Roberts, Rodney G.; Maciejewski, Anthony A.

doi:10.1109/70.143351

Cited by 57 publications

(35 citation statements)

References 9 publications

(28 reference statements)

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“…The existence of the solution of differential equations (27) has been shown in our recent work [50]. Since, the righthand side of Eq.…”

Section: Kinematically Optimal Control For the Mobile Manipulatormentioning

confidence: 99%

“…Since, the righthand side of Eq. 27 is a non-Lipschitz and complex mapping (in fact, it is discontinuous), we assume in further analysis that the solution of closed-loop system (5), (27) is unique. The aim of the further examination is to provide conditions on controller gains λ 0 , λ 1 , λ 2 , c and c 0 , which guarantee the fulfilment of equalities (11).…”

Section: Kinematically Optimal Control For the Mobile Manipulatormentioning

confidence: 99%

“…Furthermore, pseudo-inverse control strategies are not, in general, repeatable (see e.g. [26,27] for stationary robotic manipulators). A concept of repeatability for mobile manipulators was proposed, for the first time, in work [49].…”

Section: Introductionmentioning

confidence: 99%

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Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

Galicki

2018

J Intell Robot Syst

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This paper addresses the kinematically optimal control problem of the mobile manipulators. Dynamic equations of the mobile manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end-effector. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. Such controllers apply a new non-singular Terminal Sliding Mode (TSM) manifold defined by a non-linear integral equality of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, the proposed Jacobian transpose control schemes are proved to be finite-time stable provided that some well-founded assumptions are fulfilled during the mobile manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a mobile manipulator that attains trajectory tracking by the end-effector in a two-dimensional task space and simultaneously minimises some objective function.

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“…The existence of the solution of differential equations (27) has been shown in our recent work [50]. Since, the righthand side of Eq.…”

Section: Kinematically Optimal Control For the Mobile Manipulatormentioning

confidence: 99%

Section: Kinematically Optimal Control For the Mobile Manipulatormentioning

confidence: 99%

See 1 more Smart Citation

Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

Galicki

2018

J Intell Robot Syst

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“…Combinations of different methods have been developed (analytic, numerical methods; including optimization), e.g., in [10] or [11]. The Jacobian (including its inverse, resp., pseudo inverse) is also often used as, e.g., in [12]. In general, optimization methods have already been applied on the problem of inverse kinematics (e.g., [13]).…”

Section: Related Workmentioning

confidence: 99%

Estimation of inverse kinematics of arbitrary serial chain manipulators and human-like robotic hands

Petsch

Burschka

2013

2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

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Abstract-The general solution for inverse kinematics is a problem known for a long time. A lot of problems, algorithms, etc., depend on inverse kinematics. While solutions for specific serial or parallel chain manipulators exist, a good estimation for an arbitrary serial robot within a short computation time is still missing. We provide not only a tool for the discrete estimation of inverse kinematics of arbitrary serial chain manipulators, but also concepts for inverse kinematics optimization along entire paths (adaptive tunneling) and an approximation of a desired grasp with a human-like robotic hand (virtual shut grasp). The latter concept includes an efficient reduction technique of a complex, arbitrary hand, which enables a fast and accurate estimation of the inverse kinematics of an entire hand. In contrast to existing work, our approach is general, since it is neither restricted to certain configurations of the serial manipulator nor to specific structures of the hand. Moreover, our approach does neither rely on proximate starting positions nor does it require specific properties of the objective function concerning the position of the minima. It works even under the presence of multiple local minima in the solution space. Experiments show the performance of our system. The results of the estimation of the inverse kinematics are very accurate and the maximally required joint speeds along the paths are low. I. MOTIVATIONA robot which is supposed to reach a certain position with its end-effector needs to be moved to an appropriate configuration to place the end-effector in the desired position. In many situations, it is advantageous to have a system which takes the desired end-effector position as input and gives one, several or all possible goal configurations as output. The necessary mapping from the robot's workspace to its joint space is called inverse kinematics. The general solution of inverse kinematics is a known problem for a long time. Sometimes, the inverse kinematics can be computed explicitly for manipulators with certain structures. A general estimation framework for the inverse kinematics of an arbitrary serial robot is still missing. It can already be enough to know, whether a solution exits. In other cases, the knowledge about one, several or all solutions is desirable.We focus on the discrete analysis of the configurationspace. Such an analysis is, e.g., necessary for the evaluation of an arbitrary manipulator structure. We are interested in the inverse kinematics of an arbitrary serial chain manipulator at a given point without any incremental methods based on intermediate positions or (partial) derivatives (e.g., through The box should be transported. This means, first, that the object has to be grasped by the robotic hand (brown palm, magenta fingers). A serial chain manipulator has to put the hand into an appropriate position, such that a successful grasp is possible. Several configurations of the manipulator could be possible to reach a point (e.g., blue and red configurations of the...

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“…Within the domain of synthesis of Jacobian inverse kinematics algorithms the idea of shaping the algorithm's performance by combining the advantages of diverse algorithms has been fostered by Roberts and Maciejewski in a series of papers [8][9][10]. These papers addressed the problem of optimal approximation of the Jacobian pseudo inverse by a repeatable Jacobian algorithm.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach

Karpińska

Tchoń

Janiak

2012

J Intell Robot Syst

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This paper addresses the approximation problem of Jacobian inverse kinematics algorithms for redundant robotic manipulators. Specifically, we focus on the approximation of the Jacobian pseudo inverse by the extended Jacobian algorithm. The algorithms are defined as certain dynamic systems driven by the task space error, and identified with vector field distributions. The distribution corresponding to the Jacobian pseudo inverse is non-integrable, while that associated with the extended Jacobian is integrable. Two methods of devising the approximating extended Jacobian algorithm are examined. The first method is referred to as differential geometric, and relies on the approximation of a non-integrable distribution (in fact: a codistribu- tion) by an integrable one. As an alternative, the approximation problem has been formulated as the minimization of an approximation error functional, and solved using the methods of the calculus of variations. Performance of the obtained extended Jacobian inverse kinematics algorithms has been compared by means of computer simulations involving the kinematics model of the 7 dof industrial manipulator POLYCRANK. It is concluded that the differential geometric method offers a rapid, while the variational method a systematic tool for solving inverse kinematic problems.

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Nearest optimal repeatable control strategies for kinematically redundant manipulators

Cited by 57 publications

References 9 publications

Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

Estimation of inverse kinematics of arbitrary serial chain manipulators and human-like robotic hands

Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach

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