Kinematic Path Planning for Robots with Holonomic and Nonholonomic Constraints

1998 ◽  
pp. 127-150 ◽  
Author(s):  
Adam Divelbiss ◽  
Sanjeev Seereeram ◽  
John T. Wen
Keyword(s):  
Path Planning ◽  
Nonholonomic Constraints ◽  
Holonomic And Nonholonomic Constraints

Simulation of Constrained Mechanical Systems—Part II: Explicit Numerical Integration

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
David J. Braun ◽  
Michael Goldfarb
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Direct Consequence ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Constrained Motion ◽  
Constrained Mechanical Systems ◽  
Holonomic And Nonholonomic Constraints ◽  
Long Time ◽  
Constraint Correction

This paper presents an explicit to integrate differential algebraic equations (DAEs) method for simulations of constrained mechanical systems modeled with holonomic and nonholonomic constraints. The proposed DAE integrator is based on the equation of constrained motion developed in Part I of this work, which is discretized here using explicit ordinary differential equation schemes and applied to solve two nontrivial examples. The obtained results show that this integrator allows one to precisely solve constrained mechanical systems through long time periods. Unlike many other implicit DAE solvers which utilize iterative constraint correction, the presented DAE integrator is explicit, and it does not use any iteration. As a direct consequence, the present formulation is simple to implement, and is also well suited for real-time applications.

scholarly journals A new method for determining the reactions of mechanical constraints

2006 ◽  
Vol 28 (1) ◽  
pp. 35-42
Author(s):  
Do Sanh ◽  
Do Dang Khoa
Keyword(s):  
Mechanical System ◽  
Nonholonomic Constraints ◽  
Inverse Matrix ◽  
Algebraic Equations ◽  
Closed Set ◽  
Mechanical Constraints ◽  
Large Size ◽  
Holonomic And Nonholonomic Constraints ◽  
The Matrix ◽  
Lagrange’S Multipliers

In the present paper it is introduced the method for determining the reactions of mechanical constraints (holonomic and nonholonomic constraints).As is known, for studying dynamical characters of a mechanical system it is necessary to determine the constraint reactions acting on the system. Up to now, the reactions are calculated through Lagrange's multipliers. By such a way the reactions are determined only indirectly. In the [3, 4], two methods of determining directly the reactions are discussed. However, for applying these methods, it is necessary to compute the inverse matrix of the matrix of inertia. This thing in general is not convenient, specially when the matrix of inertial is of large size and dense.In the present paper it is represented the method for determining the constraint reactions, by which it is possible to avoid inertia the computation of the inverse matrix of the matrix of inertia is avoided. For this in the paper it is used the middle variables by which we obtain a closed set of algebraic equations for directly determining reactions.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

Dynamics of Nonholonomic Mechanical Systems Using a Natural Orthogonal Complement

1991 ◽  
Vol 58 (1) ◽  
pp. 238-243 ◽  
Author(s):  
Subir Kumar Saha ◽  
Jorge Angeles
Keyword(s):  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Rigid Bodies ◽  
Orthogonal Complement ◽  
Constraint Equations ◽  
Nonholonomic Mechanical Systems ◽  
Holonomic And Nonholonomic Constraints ◽  
Automatic Guided Vehicle ◽  
The Matrix ◽  
Velocity Constraint

The dynamics equations governing the motion of mechanical systems composed of rigid bodies coupled by holonomic and nonholonomic constraints are derived. The underlying method is based on a natural orthogonal complement of the matrix associated with the velocity constraint equations written in linear homogeneous form. The method is applied to the classical example of a rolling disk and an application to a 2-dof Automatic Guided Vehicle is outlined.

scholarly journals Path planning for mobile articulated robots based on the improved A* algorithm

2017 ◽  
Vol 14 (4) ◽  
pp. 172988141772801 ◽  
Author(s):  
Yaru Xu ◽  
Rong Liu
Keyword(s):  
Path Planning ◽  
Nonholonomic Constraints ◽  
Underactuated System ◽  
A Algorithm ◽  
Curvature Parameter ◽  
Turning Radius ◽  
Minimum Turning Radius ◽  
Articulated Robots ◽  
Two Parameters ◽  
Distance Parameter

Mobile articulated robots system composed of tractor and multiple articulated trailers is a nonlinear and underactuated system subject to nonholonomic constraints. The significant achievements of path planning for mobile robots with single segment are very difficult to be applied to it directly. For resolving this problem, the kinematics model is established for the system with three segments connected by nonstandard connection type, as well as its trajectory. Equivalent size is introduced that includes two parameters: the distance parameter being the size for enlarging obstacles and the curvature parameter being the minimum turning radius of system. The distance parameter is used to enlarge obstacles in the environment to shrink the system to be a particle. The planning path adopted by the improved A* algorithm can ensure itself as a collision-free and feasible path as long as the maximum path curvature is no larger than the curvature parameter in free space. The comparisons of simulation result show that the improved A* algorithm makes the quality of path optimized and more suitable than A* algorithm under the complex environment.

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