Holonomy-based motion planning of a second-order chained form system by using sinusoidal functions

2015 ◽  
Author(s):  
Masahide Ito
Keyword(s):  
Motion Planning ◽  
Second Order ◽  
Sinusoidal Functions ◽  
Form System

scholarly journals Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1337
Author(s):  
Masahide Ito
Keyword(s):  
Motion Planning ◽  
Nonholonomic Systems ◽  
Second Order ◽  
Literature Survey ◽  
First Order ◽  
Underactuated Manipulator ◽  
Planning Algorithm ◽  
The One ◽  
Specific Control ◽  
Form System

This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

scholarly journals Control Based on Linear Algebra for Trajectory Tracking and Positioning of Second-Order Chained Form System

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Leandro Rodriguez ◽  
Emanuel Serrano ◽  
Mabel Cristina Sánchez ◽  
Gustavo Scaglia
Keyword(s):  
Linear Algebra ◽  
Trajectory Tracking ◽  
Coordinate Transformation ◽  
Nonholonomic Constraints ◽  
Second Order ◽  
Reference Trajectory ◽  
Tracking Errors ◽  
Significant Interest ◽  
The Stability ◽  
Form System

The development of controllers for underactuated systems with nonholonomic constraints has been a topic of significant interest for many researchers in recent years. These systems are hard to control because their linearization transform them into uncontrollable systems. The proposed approaches involve the use of a permanent excitation in the reference trajectory; coordinate transformation; discontinuities; or complex calculations. This paper proposes the design of the controller of the second-order chained form system for trajectory tracking by using a simpler approach based on linear algebra. Up to the present time, no controllers based on this approach have been designed for that system. The control problem is solved by setting two of the three systems variables as a reference, while the remaining variable is calculated imposing the condition that the equations system has an exact solution to ensure that tracking errors go to zero. The stability of the proposed controller is theoretically demonstrated, and simulations results show a suitable control system performance. Also, no coordinate transformation is necessary.

Obstacle Avoidance Influence Coefficients for Manipulator Motion Planning

2005 ◽  
Author(s):  
Troy Harden ◽  
Chetan Kapoor ◽  
Delbert Tesar
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Minimum Distance ◽  
Higher Order ◽  
Second Order ◽  
Distance Functions ◽  
Cluttered Environments ◽  
Finite Difference Approximations ◽  
Planning Decisions ◽  
Influence Coefficients

Motion planning in cluttered environments is a weakness of current robotic technology. While research addressing this issue has been conducted, few efforts have attempted to use minimum distance rates of change in motion planning. Geometric influence coefficients provide extraordinary insight into the interactions between a robot and its environment. They isolate the geometry of distance functions from system inputs and make the higher-order properties of minimum distance magnitudes directly available. Knowledge of the higher order properties of minimum distance magnitudes can be used to predict the future obstacle avoidance, path planning, and/or target acquisition state of a manipulator system and aid in making intelligent motion planning decisions. Here, first and second order geometric influence coefficients for minimum distance magnitudes are rigorously developed for several simple modeling primitives. A general method for similar derivations using new primitives and an evaluation of finite difference approximations versus analytical second order coefficient calculations are presented. Two application examples demonstrate the utility of minimum distance magnitude influence coefficients in motion planning.

Control and Motion Planning of a Nonholonomic Parallel Orienting Platform

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Janusz Jakubiak ◽  
Władyslaw Magiera ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Translational Motion ◽  
Open Loop ◽  
Planning Algorithm ◽  
Parallel Platform ◽  
Practical Stabilization ◽  
Planning Problems ◽  
Form System ◽  
Loop Motion ◽  
Space Approach

An orienting platform is a mechanism which allows rotation of a spatial object without translational motion of that object. In this work, we study a parallel platform with one passive nonholonomic spherical joint and two series of spherical, actuated prismatic and universal joints (the platform is also known in literature as an (nS)-2SPU wrist). To solve the control and motion planning problems, an analytic approach is used. The design of practical stabilization and tracking algorithm is based on transverse functions and a method for motion planning respecting mechanical singularities is derived from endogenous configuration space approach. It is shown that the system is controllable and locally equivalent to the chained form system. Then, the stabilization, tracking, and motion planning algorithms are proposed. Results are verified with computer simulations. A combination of the open-loop motion planning algorithm and the closed-loop tracking provide a tool for designing a motion planning algorithm respecting mechanical singularities and robust to input disturbances.

Linear Algebra Based Control: Application to a second order chained form system

2021 ◽  
Vol 19 (9) ◽  
pp. 1435-1442
Author(s):  
Leandro Pedro Faustino Rodriguez Aguilar ◽  
Maria Cecilia Fernandez Puchol ◽  
Mabel Cristina Sanchez ◽  
Gustavo Javier Scaglia
Keyword(s):  
Linear Algebra ◽  
Second Order ◽  
Control Application ◽  
Form System

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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