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A jacobian-based algorithm for planning the motion of an underactuated rigid body undergoing forward and reverse rotations

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ROBOTICA 2010年第5期28卷 747-757页

作者： Koh, Sung K. Pohang Univ Sci & Technol Dept Mech Engn Pohang South Korea

A jacobian-based algorithm that is useful for planning the motion of a floating rigid body operated using two input torques is addressed in this paper. The rigid body undergoes a four-rotation fully reversed (FR) sequence of rotations which consists of two initial rotations about the axes of a coordinate frame attached to the body and two subsequent rotations that undo the preceding rotations. Although a jacobian-based algorithm has been useful in exploring the inverse kinematics of conventional robot manipulators, it is not apparent how a correct FR sequence for a desired orientation could be found because the jacobian of FR sequences is singular as well as being a null matrix at the identity. To discover the FR sequences that can synthesize the desired orientation circumventing these difficulties, the jacobian algorithm is reformulated and implemented from arbitrary orientations where the jacobian is not singular. Due to the insufficient degrees-of-freedom of four-rotation FR sequences required to achieve all possible orientations, the rigid body cannot achieve certain orientations in the configuration space. To best approximate these infeasible orientations, the jacobian-based algorithm is implemented in the sense of least squares. As some orientations can never be attained by a single four-rotation FR sequence, two different four-rotation FR sequences are exploited alternately to ensure the convergence of the proposed algorithm. Assuming the orientation is supposed to be manipulated using three input torques, the switching jacobian algorithm proposed in this paper has significant practical importance in planning paths for aerospace and underwater vehicles which are maneuvered using only two input torques due to the failure of one of the torque-generation mechanisms.

关键词： Underactuated system Attitude control Fully reversed sequences of rotations Noncommutativity of finite rigid rotations jacobian algorithm Motion planning

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A jacobian-Based algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

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JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS 2009年第1期4卷 11012-11012页

作者： Koh, Sung K. Chirikjian, Gregory S. Ananthasuresh, G. K. Pohang Univ Sci & Technol Dept Mech Engn Pohang 790784 South Korea Johns Hopkins Univ Dept Mech Engn Baltimore MD 21218 USA Indian Inst Sci Dept Mech Engn Bangalore 560012 Karnataka India

algorithms for planning quasistatic attitude maneuvers based on the jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the jacobian of conventional systems such as a robot manipulator, the jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional jacobian formulation. Therefore, the jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the jacobian is singular or null. [DOI: 10.1115/1.3007903]

关键词： attitude control fully-reversed sequences of rotations noncommutativity of finite rigid rotations jacobian algorithm inverse kinematics motion planning

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Global convergence of adjoint jacobian motion planning algorithm for the Chaplygin sleigh

Global convergence of adjoint Jacobian motion planning algor...

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作者： Malek, Lukasz Institute of Computer Engineering Control and Robotics Wroclaw University of Technology Wroclaw Poland

This paper is concerned with the adjoint jacobian motion planning algorithm for the Chaplygin sleigh. We introduce general idea about the algorithm and prove completeness of this algorithm for the Chaplygin sleigh. Fi... 详细信息

ISBN: (纸本)9783902661555

关键词： Chaplygin sleigh jacobian algorithm Motion planning Nonholonomic system

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Global Convergence of Adjoint jacobian Motion Planning algorithm for the Chaplygin Sleigh

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IFAC Proceedings Volumes 2009年第13期42卷 659-664页

作者： Lukasz Malek Institute of Computer Engineering Control and Robotics Wroclaw University of Technology Wroclaw Poland

Abstract This paper is concerned with the adjoint jacobian motion planning algorithm for the Chaplygin sleigh. We introduce general idea about the algorithm and prove completeness of this algorithm for the Chaplygin s... 详细信息

关键词： Chaplygin sleigh nonholonomic system motion planning jacobian algorithm

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Approximation of jacobian Inverse Kinematics algorithms: Differential Geometric vs. Variational Approach

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JOURNAL OF INTELLIGENT & ROBOTIC SYSTEMS 2012年第3-4期68卷 211-224页

作者： Karpinska, Joanna Tchon, Krzysztof Janiak, Mariusz Wroclaw Univ Technol Inst Comp Engn Control & Robot PL-50372 Wroclaw Poland

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 codistribution) 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.

关键词： Redundant manipulator Inverse kinematics jacobian algorithm Approximation Distribution Minimization

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Dynamically consistent jacobian inverse for mobile manipulators

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INTERNATIONAL JOURNAL OF CONTROL 2016年第6期89卷 1159-1168页

作者： Ratajczak, Joanna Tchon, Krzysztof Wroclaw Univ Technol Elect Fac PL-50370 Wroclaw Poland

By analogy to the definition of the dynamically consistent jacobian inverse for robotic manipulators, we have designed a dynamically consistent jacobian inverse for mobile manipulators built of a non-holonomic mobile platform and a holonomic on-board manipulator. The endogenous configuration space approach has been exploited as a source of conceptual guidelines. The new inverse guarantees a decoupling of the motion in the operational space from the forces exerted in the endogenous configuration space and annihilated by the dual jacobian inverse. A performance study of the new jacobian inverse as a tool for motion planning is presented.

关键词： kinematics endogenous configuration space approach jacobian algorithm Mobile manipulator dynamic consistency motion planning

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Iterative learning control and the singularity robust jacobian inverse for mobile manipulators

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INTERNATIONAL JOURNAL OF CONTROL 2010年第11期83卷 2253-2260页

作者： Tchon, Krzysztof Wroclaw Univ Technol Inst Comp Engn Control & Robot PL-50372 Wroclaw Poland

The method of iterative learning control, to a large extent, has been inspired by robotics research, focused on the control of stationary manipulators. In this article we deal with the inverse kinematics problem for mobile manipulators, and show that a very basic singularity robust jacobian inverse can be derived in a natural way within the framework of iterative learning control. To achieve this objective we have exploited the endogenous configuration space approach. The introduced jacobian inverse defines the singularity robust jacobian inverse kinematics algorithm for mobile manipulators. A Kantorovich-type estimate of the region of guaranteed convergence of the algorithm is derived. For two example kinematics, this estimate has been computed efficiently.

关键词： mobile manipulator inverse kinematics iterative learning control jacobian algorithm

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General Lagrange-Type jacobian Inverse for Nonholonomic Robotic Systems

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IEEE TRANSACTIONS ON ROBOTICS 2018年第1期34卷 256-263页

作者： Tchon, Krzysztof Ratajczak, Joanna Wroclaw Univ Sci & Technol Chair Cybernet & Robot Elect Fac PL-50372 Wroclaw Poland

This paper discusses the nonholonomic robotic systems whose motion constraints assume the Pfaffian form, and the equations of motion are represented by driftless control systems with outputs. By reference to the end point map of such a control system, we define the system's jacobian and study jacobian motion-planning algorithms. A new Lagrange-type jacobian inverse, referred to as the General Lagrangian jacobian Inverse (GLJI), is designed as the solution of an optimal control problem with a Lagrange-type objective function. Singularities of GLJI are examined. A special choice of the objective function illustrates features of GLJI. A new motion-planning algorithm based on GLJI is proposed. Theoretical arguments are illustrated with a motion-planning problem of a space robot.

关键词： jacobian algorithm motion-planning nonholonomic system optimal control singularities

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Lagrangian jacobian inverse for nonholonomic robotic systems

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NONLINEAR DYNAMICS 2015年第4期82卷 1923-1932页

作者： Tchon, Krzysztof Ratajczak, Adam Goral, Ida Wroclaw Univ Technol Elect Fac Chair Cybernet & Robot PL-50372 Wroclaw Poland Wroclaw Univ Technol Elect Fac Chair Automat Mechatron & Control Syst PL-50372 Wroclaw Poland

The motion planning problem for nonholonomic robotic systems is studied using the continuation method and the optimization paradigms. A new jacobian motion planning algorithm is derived, based on a solution of the Lagrange-type optimization problem addressed in the linear approximation of the system. Performance of the new algorithm is illustrated by numeric computations performed for the unicycle robot kinematics.

关键词： Nonholonomic system Motion planning jacobian algorithm Optimization

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Lagrangian jacobian Motion Planning: A Parametric Approach

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JOURNAL OF INTELLIGENT & ROBOTIC SYSTEMS 2017年第3-4期85卷 511-522页

作者： Goral, Ida Tchon, Krzysztof Wroclaw Univ Technol Chair Cybernet & Robot Elect Fac Ul Janiszewskiego 11-17 PL-50372 Wroclaw Poland

This paper addresses the motion planning problem of nonholonomic robotic systems. The system's kinematics are described by a driftless control system with output. It is assumed that the control functions are represented in a parametric form, as truncated orthogonal series. A new motion planning algorithm is proposed based on the solution of a Lagrange-type optimisation problem stated in the linear approximation of the parametrised system. Performance of the algorithm is illustrated by numeric computations for a motion planning problem of the rolling ball.

关键词： jacobian algorithm Motion planning Nonholonomic system Parametrisation

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