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

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe 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.

scholarly journals Multiple-task motion planning of non-holonomic systems with dynamics

2013 ◽  
Vol 4 (1) ◽  
pp. 153-166 ◽  
Author(s):  
A. Ratajczak ◽  
K. Tchoń
Keyword(s):  
Motion Planning ◽  
Robotic Systems ◽  
Planning Problem ◽  
Snake Robot ◽  
Affine System ◽  
Planning Task ◽  
Robot Performance ◽  
Multiple Task ◽  
Space Approach ◽  
Motion Planning Problem

Abstract. This paper addresses the motion planning problem in non-holonomic robotic systems. The system's kinematics and dynamics are represented as a control affine system with outputs. The problem is defined in terms of the end-point map of this system, using the endogenous configuration space approach. Special attention is paid to the multiple-task motion planning problem, i.e. a problem that beyond the proper motion planning task includes a number of additional tasks. For multiple-task motion planning two strategies have been proposed, called the egalitarian approach and the prioritarian approach. Also, two computational strategies have been launched of solving the motion planning problem: the parametric and the non-parametric. The motion planning and computational strategies have been applied to a motion planning problem of the trident snake robot. Performance of the motion planning algorithms is illustrated with computer simulations.

scholarly journals On dynamically consistent Jacobian inverse for non-holonomic robotic systems

2017 ◽  
Vol 27 (4) ◽  
pp. 555-573 ◽  
Author(s):  
Joanna Ratajczak ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Consistency Condition ◽  
Robotic Systems ◽  
Planning Problem ◽  
Commutativity Property ◽  
Kinematic Singularities ◽  
Planning Problems ◽  
Jacobian Inverse ◽  
Space Approach

AbstractThis paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem. The system’s kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system’s dynamics. The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered.

On the Normal Forms Associated with High Dimensional Systems

2000 ◽  
Vol 123 (2) ◽  
pp. 157-169 ◽  
Author(s):  
Koncay Huseyin ◽  
Weiyi Zhang
Keyword(s):  
Nonlinear Systems ◽  
Normal Form ◽  
Normal Forms ◽  
High Dimensional ◽  
Engineering Applications ◽  
Modified Normal Form Approach ◽  
Form Approach

In this paper, a modified normal form approach is proposed for the analysis of high dimensional nonlinear systems. Using the modified approach, calculations of normal forms and, in particular, the related coefficients are carried out much more conveniently. Certain high dimensional systems, including systems with inner resonances, are investigated. These systems exist widely in engineering applications. To illustrate the approach, five examples are presented.

Task-priority motion planning of underactuated systems: an endogenous configuration space approach

Robotica ◽  
2009 ◽  
Vol 28 (6) ◽  
pp. 885-892 ◽  
Author(s):  
Adam Ratajczak ◽  
Joanna Karpińska ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Robotic Systems ◽  
Planning Problem ◽  
Redundant Manipulators ◽  
Container Ship ◽  
Secondary Tasks ◽  
Planning Algorithm ◽  
Task Priority ◽  
Space Approach

SUMMARYThis paper presents a task-priority motion planning algorithm for underactuated robotic systems. The motion planning algorithm combines two features: the idea of the task-priority control of redundant manipulators and the endogenous configuration space approach. This combination results in the algorithm which solves the primary motion planning task simultaneously with one or more secondary tasks ordered in accordance with decreasing priorities. The performance of the task-priority motion planning algorithm has been illustrated with computer simulations of the motion planning problem for a container ship.

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

NORMAL FORMS FOR FUZZY LOGIC — AN APPLICATION OF KOLMOGOROV’S THEOREM

1996 ◽  
Vol 04 (04) ◽  
pp. 331-349 ◽  
Author(s):  
VLADIK KREINOVICH ◽  
HUNG T. NGUYEN ◽  
DAVID A. SPRECHER
Keyword(s):  
Neural Networks ◽  
Fuzzy Logic ◽  
Normal Form ◽  
Normal Forms ◽  
Approximation Property ◽  
Universal Approximation ◽  
Approximation Result ◽  
Logical Operations ◽  
Kolmogorov's Theorem

This paper addresses mathematical aspects of fuzzy logic. The main results obtained in this paper are: 1. the introduction of a concept of normal form in fuzzy logic using hedges; 2. using Kolmogorov’s theorem, we prove that all logical operations in fuzzy logic have normal forms; 3. for min-max operators, we obtain an approximation result similar to the universal approximation property of neural networks.

Motion Planning of a Nonholonomic Multibody System Using Genetic Algorithm

2003 ◽  
Author(s):  
Xin-Sheng Ge ◽  
Li-Qun Chen
Keyword(s):  
Genetic Algorithm ◽  
Motion Planning ◽  
Nonholonomic System ◽  
Multibody System ◽  
Planning Problem ◽  
Control Approach ◽  
Velocity Constraints ◽  
Nonholonomic Motion Planning ◽  
Optimal Control Approach ◽  
Motion Planning Problem

The motion planning problem of a nonholonomic multibody system is investigated. Nonholonomicity arises in many mechanical systems subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the control problem of system can be converted to the motion planning problem for a driftless control system. In this paper, we propose an optimal control approach for nonholonomic motion planning. The genetic algorithm is used to optimize the performance of motion planning to connect the initial and final configurations and to generate a feasible trajectory for a nonholonomic system. The feasible trajectory and its control inputs are searched through a genetic algorithm. The effectiveness of the genetic algorithm is demonstrated by numerical simulation.

Motion planning problem with obstacle avoidance for step-2 bracket-generating systems

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 799-800 ◽  
Author(s):  
Victoria Grushkovskaya ◽  
Alexander Zuyev
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Planning Problem ◽  
Motion Planning Problem
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