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.

Probabilistic Roadmaps Based Motion Planning of a 4 Degree of Freedom Robot

2012 ◽  
Vol 241-244 ◽  
pp. 1922-1930
Author(s):  
Yu Tian Liu
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Shortest Path ◽  
Degrees Of Freedom ◽  
Learning Phase ◽  
Degree Of Freedom ◽  
Motion Path ◽  
Probabilistic Roadmaps ◽  
Two Phases ◽  
4 Degrees Of Freedom

In this paper, we used a probabilistic roadmaps(PRM) method to plan a motion path for a 4 degrees of freedom(DOF) robot in static workspace. This methods includes two phases: a learning phase and a query phase. In learning phase, a roadmap is constructed and stored as a graph , in which stores all of the random collision-free configurations in free configuration space denoted by and keeps all of the edges corresponding to feasible paths between these configurations. In query phase, the algorithm tries to connect any given initial and goal configuration to the nodes in the graph. And then the Dijkstra's algorithm searches for a shortest path to concatenate these two nodes. The experiment result demonstrates that this method applying to this 4 degrees of freedom robot works well.

Motion planning in crowded planar environments

Robotica ◽  
1999 ◽  
Vol 17 (4) ◽  
pp. 365-371 ◽  
Author(s):  
Yoav Lasovsky ◽  
Leo Joskowicz
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Local Geometry ◽  
Objective Functions ◽  
Linear Optimization Problems ◽  
Geometrically Complex ◽  
Crowded Environments

We present a new algorithm for fine motion planning in geometrically complex situations. Geometrically complex situations have complex robot and environment geometry, crowded environments, narrow passages and tight fits. They require complex robot motions with coupled degrees of freedom. The algorithm constructs a path by incrementally building a graph of linearized convex configuration space cells and solving a series of linear optimization problems with varying objective functions. Its advantages are that it better exploits the local geometry of narrow passages in configuration space, and that its complexity does not significantly increase as the clearance of narrow passages decreases. We demonstrate the algorithm on examples which other planners could not solve.

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.

A real-time motion planning algorithm for a hyper-redundant set of mechanisms

Robotica ◽  
2013 ◽  
Vol 31 (8) ◽  
pp. 1327-1335 ◽  
Author(s):  
Nir Shvalb ◽  
Boaz Ben Moshe ◽  
Oded Medina
Keyword(s):  
Motion Planning ◽  
Real Time ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Morse Function ◽  
Climbing Robot ◽  
Probabilistic Algorithm ◽  
Road Map ◽  
Time Motion ◽  
Planning Algorithm

SUMMARYWe introduce a novel probabilistic algorithm (CPRM) for real-time motion planning in the configuration space${\EuScript C}$. Our algorithm differs from a probabilistic road map (PRM) algorithm in the motion between a pair of anchoring points (local planner) which takes place on the boundary of the obstacle subspace${\EuScript O}$. We define a varying potential fieldfon ∂${\EuScript O}$as a Morse function and follow$\vec{\nabla} f$. We then exemplify our algorithm on a redundant worm climbing robot withndegrees of freedom and compare our algorithm running results with those of the PRM.

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.

ANALISA PENGARUH IKLIM ORGANISASI DAN KOMPETENSI TERHADAP KINERJA PEGAWAI PT HUTAMA KARYA

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Erik Wardhana, MM.
Keyword(s):  
Organizational Climate ◽  
Employee Performance ◽  
Sampling Technique ◽  
Simple Random Sampling ◽  
Free Variable ◽  
Independent Variables ◽  
Dependent Variables ◽  
Correlational Approach ◽  
Survey Research Methods ◽  
The Relationship

This study entitled "Analysis of Effect of Climate Organization and Competence Againt Employee PT. Hutama Karya ". The purpose of this study was to obtain information on the relationship between the free variable that organizational climate (X1) and competence (X2) with the dependent variable is employee performance (Y), either partially or simultaneously, This study used survey research methods with the correlational approach and predictive, which aims for the relationship and influence between independent and dependent variables. The sampling technique can be done randomly (simple random sampling) of 852 employees, which is considered to resprentatif is 89 people. And to solve problems, to analyze and examine the relationship and influence between the independent variables on the dependent variable used models kausalistik through regression analysis with SPSS 14.0

PENGARUH PERSONAL BACKGROUND, POLITICAL BACKGROUND DAN PENGEATAHUAN DEWAN TENTANG ANGGARAN TERHADAP PERAN DPRD DALAM PENGAWASAN KEUANGAN DAERAH

2008 ◽  
Author(s):  
Yesi Mutia Basri ◽  
Rosliana Rosliana
Keyword(s):  
Multivariate Analysis ◽  
Significant Influence ◽  
Political Activity ◽  
Primary Data ◽  
Financial Control ◽  
Independent Variables ◽  
Dependent Variables ◽  
Political Background ◽  
Activity Dependent

This research aim to examine the influence of personal background, political background, and council budget knowledge towards the role of DPRD on region financial control. This research is motivated by the fact that individual background will effect to individual behavior on political activity. Dependent variables in this research are personal background, political background, and council budges knowledge towards the role of DPRD on region financial control Independent variables are the role of DPRD on region financial control in planning, implementing, and responsibility steps. The data in this research consist of primary data that taken from questionnaires distributed directly to respondents. The collected are from 34 Respondents that members of DPRD at Pekanbaru. Hypothesis of this research are examine by using Multivariate Analysis of Variances (MANOVA). The result of this research HI personal background political background and budget knowledge have significant influence toward the role of DPRD on region financial control in planning steps.H2 personal background, politico I background and budget knowledge have no significant influence toward the role of DPRD on region financial control in Implementing steps. H3 personal background political background and budget knowledge have no significant influence toward the role of DPRD on region financial control in Controlling steps.

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