Lagrangian Jacobian inverse for nonholonomic robotic systems

Tchoń, Krzysztof; Ratajczak, Adam; Góral, Ida

doi:10.1007/s11071-015-2288-6

Cited by 12 publications

(6 citation statements)

References 21 publications

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“…4. c 1 = 1 and c 2 = 3 were used as the values of hyperparameters in (16). During simulations, the initial configuration of the joints is assumed to be home configuration, i.e., all joint angles are zero.…”

Section: B Trajectory Tracking Resultsmentioning

confidence: 99%

“…5. Similar to the case of rectangular trajectory, c 1 = 1 and c 2 = 3 were used as the values of hyperparameters in (16). Fig.…”

Section: B Trajectory Tracking Resultsmentioning

confidence: 99%

“…The BAORNN algorithm works by generating a random direction vector b ∈ Algorithm 1: BAORNN algorithm Input: A m-DOF robotic arm with unknown kinematic model attached with position and orientation sennsors, a reference trajectory x r (t) ∈ R n for end-effector and an objective function g(x r (t), θ(t)) quantifying the quality of tracking performance. Additionally, the values of hyper-parameters: c 1 and c 2 defined in (16). Output: An optimal trajectory θ r (t) in joint space.…”

Section: A Algorithm Formulationmentioning

confidence: 99%

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Using Social Behavior of Beetles to Establish a Computational Model for Operational Management

Khan

Cao

et al. 2020

IEEE Trans. Comput. Soc. Syst.

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In this paper, we computationally model the social behavior of beetles and apply it to the tracking control of manipulators. The beetles demonstrate excellent skills to forage food in a previously unknown environment by merely using their olfactory senses. The goal of the beetle is to search the region with the maximum smell. Therefore, the actions of the beetle can be characterized as an optimization algorithm. This paper mathematically models this behavior in the form of a Recurrent Neural Network (RNN) with a temporal-feedback connection. We apply the formulated RNN controller for the redundancy resolution and tracking control of the redundant manipulators with an unknown kinematic model. Most of the industrial robots have redundant manipulators, and kinematic trajectory tracking is a fundamental problem for any industrial task. The behavior of the beetle allows us to formulate a position-level controller without relying on the manipulation of the Jacobian matrix. It is in contrast with the conventional velocity-level controllers, which require an accurate kinematic model of the manipulator and calculation of pseudo-inverse of Jacobian, a computationally expensive task. The proposed algorithm, called Beetle Antennae Olfactory Recurrent Neural Network (BAORNN) algorithm; is capable of driving the manipulator by only using the feedback from the position and orientation sensors. The stability and convergence of the proposed algorithm are theoretically proved, and simulations results using a 7-DOF industrial robotic arm, KUKA LBR IIWA14, are presented to demonstrate the performance of the proposed algorithm.Legend: † g(x) denotes the intensity of smell. ‡ Color intensity ∝ g(x).

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Section: B Trajectory Tracking Resultsmentioning

confidence: 99%

“…5. Similar to the case of rectangular trajectory, c 1 = 1 and c 2 = 3 were used as the values of hyperparameters in (16). Fig.…”

Section: B Trajectory Tracking Resultsmentioning

confidence: 99%

Section: A Algorithm Formulationmentioning

confidence: 99%

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Using Social Behavior of Beetles to Establish a Computational Model for Operational Management

Khan

Cao

et al. 2020

IEEE Trans. Comput. Soc. Syst.

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“…Given the joint velocities, the torque level motion planning has been reduced to the standard inverse dynamics problem for the on-board manipulator. The efficiency of the NFA to motion planning has been demonstrated by numeric computations, whose results have been compared with a solution of the motion planning problem provided by the Endogenous Configuration Space Approach (ECSA), an iterative method of motion planning for non-holonomic robotic systems, based on the concept of robot's Jacobian [21]. From the results of computations one can learn that in space applications the NFA distinguishes by its accuracy and efficiency, however, may encounter difficulties concerned with computability, complexity, and local existence of the feedback transformations.…”

Section: Introductionmentioning

confidence: 99%

Normal form approach in the motion planning of space robots: a case study

Tchoń

Zadarnowska

2021

Nonlinear Dyn

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We examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

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“…In this way the Jacobian pseudoinverse is obtained. As a natural generalization, in [10] we have designed a Lagrangian Jacobian inverse, based on the minimisation of the Lagrangian objective function, which takes into consideration both the control and the trajectory of the the linearised system. This new inverse leads to the Lagrangian Jacobian motion planning algorithm.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian Jacobian Motion Planning: A Parametric Approach

Góral

Tchoń

2016

J Intell Robot Syst

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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.

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Lagrangian Jacobian inverse for nonholonomic robotic systems

Cited by 12 publications

References 21 publications

Using Social Behavior of Beetles to Establish a Computational Model for Operational Management

Using Social Behavior of Beetles to Establish a Computational Model for Operational Management

Normal form approach in the motion planning of space robots: a case study

Lagrangian Jacobian Motion Planning: A Parametric Approach

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