A Lie algebraic method of motion planning for driftless nonholonomic systems

2005 ◽  
Author(s):  
I. Duleba ◽  
W. Khefifi
Keyword(s):  
Motion Planning ◽  
Algebraic Method ◽  
Nonholonomic Systems

Layer, Lie algebraic method of motion planning for nonholonomic systems

2012 ◽  
Vol 349 (1) ◽  
pp. 201-215 ◽  
Author(s):  
Ignacy Duleba ◽  
Wissem Khefifi ◽  
Iwona Karcz-Duleba
Keyword(s):  
Motion Planning ◽  
Algebraic Method ◽  
Nonholonomic Systems

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.

Motion Planning of Nonholonomic Systems with Tracking Control Lyapunov Function

2010 ◽  
Vol 44-47 ◽  
pp. 3992-3996
Author(s):  
Yan Peng ◽  
Mei Liu ◽  
Zhi Jie Tang ◽  
Shao Rong Xie ◽  
Jun Luo
Keyword(s):  
Lyapunov Function ◽  
Motion Planning ◽  
Tracking Control ◽  
Degrees Of Freedom ◽  
Nonholonomic Constraint ◽  
Trajectory Generation ◽  
Nonholonomic Systems ◽  
Control Lyapunov Function ◽  
Dynamical Degrees

A common approach to motion planning of robots and vehicles involves finding suitable trajectories for the positions of each configuration variable, and then using feedback to regulate the system to these trajectories. However, when the system has less actuator than dynamical degrees of freedom, it is not always possible to do this arbitrarily. In this paper a tracking control Lyapunov function (TCLF) is proposed to guarantee that the trajectory generation is convergent and executable under nonholonomic constraint, and the simulation result conducted on surface vehicle shows its effectiveness.

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.

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