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 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.

Modified PD Control of Rotary Inverted Pendulum

2009 ◽  
Author(s):  
Naserodin Sepehry ◽  
Mahnaz Shamshirsaz
Keyword(s):  
Feedback Control ◽  
Inverted Pendulum ◽  
Break Point ◽  
State Feedback Control ◽  
Pd Controller ◽  
Loop Transfer Function ◽  
Full State ◽  
Full State Feedback ◽  
Rotary Inverted Pendulum ◽  
Space Method

The inverted pendulum, a classical mechatronic application, exists in many different forms. In despite that many works have been done to balance the pendulum link on end of this device using feedback control but few studies have been developed to control this rotary inverted pendulum using PD controller. In classical methods, using PD, PI or PID control, difficulties appear due to one of the coefficients becomes zero in closed loop transfer function denominator and consequently the system becomes unstable. In this study, an arbitrary pole is placed in order to create a break point in root locus, so by this way a PD controller can be designed for this new system. Also, disturbance rejection has been investigated by state space method in this paper. The results of this modified PD controller are compared with full state feedback control and optimal control, so the method used in this study has been validated.

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