Related papers: Structure of Motion under Constraints and non-Holo…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
Accurately following a geometric desired path in a two-dimensional space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to…
We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…
Many robotic systems allow independent control of position and orientation (pose), including omnidirectional aerial vehicles, underwater robots, and manipulator end-effectors. In many applications, these systems must follow a continuous…
Using a designed vector field to control a mobile robot to follow a given desired path is intuitive and practical, and to build a rigorous theory to guide its implementation is essential. In this paper, we study the properties of a general…
A path-following control algorithm enables a system's trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence…
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints…
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a…
I consider the equations of motion which follow from d'Alembert's principle for a general mechanical system in a space of N dimensions, constrained by a non-holonomic constraint which is linear and homogeneous in the generalised velocities.…
This paper focuses on the motion planning for mobile robots in 3D, which are modelled by 6-DOF rigid body systems with nonholonomic kinematics constraints. We not only specify the target position, but also bring in the requirement of the…
In the vector-field guided path-following problem, a sufficiently smooth vector field is designed such that its integral curves converge to and move along a one-dimensional geometric desired path. The existence of singular points where the…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
Vector fields are advantageous in handling nonholonomic motion planning as they provide reference orientation for robots. However, additionally incorporating curvature constraints becomes challenging, due to the interconnection between the…
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic…
The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the…
In this paper we propose an algorithm for path following control of the nonholonomic mobile robot based on the idea of the guiding vector field (GVF). The desired path may be an arbitrary smooth curve in its implicit form, that is, a level…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…