Motion Planning of Nonholonomic Systems – Nondeterministic Endogenous Configuration Space Approach

2012 ◽  
pp. 305-315 ◽  
Author(s):  
Mariusz Janiak
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Nonholonomic Systems ◽  
Space Approach

Motion planning of the trident snake robot equipped with passive or active wheels

2012 ◽  
Vol 60 (3) ◽  
pp. 547-555 ◽  
Author(s):  
D. Paszuk ◽  
K. Tchoń ◽  
Z. Pietrowska
Keyword(s):  
Control System ◽  
Motion Planning ◽  
Computer Simulations ◽  
Configuration Space ◽  
Snake Robot ◽  
System Representation ◽  
And Control ◽  
Planning Problems ◽  
Jacobian Algorithm ◽  
Space Approach

Abstract We study the kinematics of the trident snake robot equipped with either active joints and passive wheels or passive joints and active wheels. A control system representation of the kinematics is derived, and control singularities examined. Two motion planning problems are addressed, corresponding to diverse ways of controlling the robot, and solved by means of the endogenous configuration space approach. The constraints imposed by the presence of control singularities are handled using the imbalanced Jacobian algorithm assisted by an auxiliary feedback. Performance of the motion planning algorithms is demonstrated by computer simulations.

Velocity space approach to motion planning of nonholonomic systems

Robotica ◽  
2007 ◽  
Vol 25 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Ignacy Duleba ◽  
Wissem Khefifi
Keyword(s):  
Motion Planning ◽  
Inverted Pendulum ◽  
Nonholonomic Systems ◽  
Velocity Space ◽  
Space Method ◽  
Space Approach

SUMMARYIn this paper, a velocity space method of motion planning for nonholonomic systems is presented. This method, based on Lie algebraic principles and locally around consecutive current states, plans a motion towards a goal. It is effective as most of the computations can be carried out analytically. This method is illustrated on the unicycle robot and the inverted pendulum.

scholarly journals Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method

2021 ◽  
Vol 11 (21) ◽  
pp. 10245
Author(s):  
Arkadiusz Mielczarek ◽  
Ignacy Dulęba
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Algebraic Method ◽  
Nonholonomic Systems ◽  
Inverse Kinematic ◽  
General Purpose ◽  
Task Space ◽  
Local Motion ◽  
Planning Algorithm ◽  
Nonholonomic Motion Planning

In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly.

A Surface Integral Approach to the Motion Planning of Nonholonomic Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 315-325 ◽  
Author(s):  
Ranjan Mukherjee ◽  
David P. Anderson
Keyword(s):  
Motion Planning ◽  
Surface Area ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Nonholonomic Systems ◽  
Integral Approach ◽  
Surface Integral ◽  
Independent Variables ◽  
Dependent Variables ◽  
Disk Rolling

Nonholonomic mechanical systems are governed by constraints of motion that are nonintegrable differential expressions. Unlike holonomic constraints, these constraints do not reduce the number of dimensions of the configuration space of a system. Therefore a nonholonomic system can access a configuration space of dimension higher than the number of the degrees of freedom of the system. In this paper, we develop an algorithm for planning admissible trajectories for nonholonomic systems that will take the system from one point in its configuration space to another. In our algorithm the independent variables are first converged to their desired values. Subsequently, closed trajectories of the independent variables are used to converge the dependent variables. We use Green’s theorem in our algorithm to convert the problem of finding a closed path into that of finding a surface area in the space of the independent variables such that the dependent variables converge to their desired values as the independent variables traverse along the boundary of this surface area. Using this approach, we specifically address issues related to the reachability of the system, motion planning amidst additional constraints, and repeatable motion of nonholonomic systems. The salient features of our algorithm are quite apparent in the two examples we discuss: a planar space robot and a disk rolling without slipping on a flat surface.

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.

scholarly journals Task-priority motion planning of underactuated systems: an endogenous configuration space approach – ERRATUM

Robotica ◽  
2010 ◽  
Vol 28 (6) ◽  
pp. 943-943
Author(s):  
Adam Ratajczak ◽  
Joanna Karpińska ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Underactuated Systems ◽  
Single Task ◽  
Correct Form ◽  
Task Priority ◽  
Image Position ◽  
Priority Algorithm ◽  
Space Approach

Figures 2 and 5 were incorrectly reproduced in the above publication (Ratajczak et al. 2009). The figures are reproduced below in their correct form. Fig. 2.Task-priority algorithm (both S1 and S2).Fig. 5.Single-task algorithm (only S1).

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.

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