Motion Planning and Posture Control of Multiple n-link Doubly Nonholonomic Manipulators

The paper considers the problem of motion planning and posture control of multiple n-link doubly nonholonomic mobile manipulators in an obstacle-cluttered and bounded workspace. The workspace is constrained with the existence of an arbitrary number of fixed obstacles (disks, rods and curves), artificial obstacles and moving obstacles. The coordination of multiple n-link doubly nonholonomic mobile manipulators subjected to such constraints becomes therefore a challenging navigational and steering problem that few papers have considered in the past. Our approach to developing the controllers, which are novel decentralized nonlinear acceleration controllers, is based on a Lyapunov control scheme that is not only intuitively understandable but also allows simple but rigorous development of the controllers. Via the scheme, we showed that the avoidance of all types of obstacles was possible, that the manipulators could reach a neighborhood of their goal and that their final orientation approximated the desired orientation. Computer simulations illustrate these results. KEYWORDS: Lyapunov-based control scheme; Doubly nonholonomic manipulators; Ghost parking bays; Minimum distance technique; Stability; Kinodynamic constraints

Potential field functions for motion planning and posture of the standard 3 - trailer system

This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of 3-trailer systems in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. The effectiveness of the proposed control laws were demonstrated via simulations of two traffic scenarios

Formation control of mobile robots

In this paper, we study the formation control problem for car-like mobile robots. A team of nonholonomic mobile robots navigate in a terrain with obstacles, while maintaining a desired formation, using a leader-following strategy. A set of artificial potential field functions is proposed using the direct Lyapunov method for the avoidance of obstacles and attraction to their designated targets. The effectiveness of the proposed control laws to verify the feasibility of the model is demonstrated through computer simulations

Spaces of initial values of differential equations with the Painlevé property

In this thesis, we study the spaces of initial values of some differential equations with the Painlevé property. The first part of our study begins by introducing the standard techniques associated with such spaces by discussing the well known example of the second Painlevé equation P_II. We then apply these techniques to the cases of linearisable second-order ordinary differential equations (ODEs) and a fourth-order analogue of P_II with particular emphasis on the solutions and structure of the singularities. We explicitly show that the initial value spaces of these ODEs can be regularised for family of general solutions while special family of solutions containing fewer free parameters than the equations’ orders require an infinite number of resolutions or blow ups. To complement our study, we also consider the spaces of initial values of partial differential equations (PDEs). Our examples are Burgers’ and the Korteweg-de Vries equations, whose movable singularities are described by Laurent expansions of the solutions around an arbitrary noncharacteristic manifold. We embed the initial values of these PDEs in complex projective spaces of the appropriate respective dimension and resolve base loci in the corresponding space. As in the ODE case, the initial value space is best understood as a foliation. It is interesting to observe that for both the PDEs, generic initial values are resolved by a finite number of blow ups, while certain initial values lead to an infinite number of blow ups. We provide evidence to show that the latter cases correspond to implicit special solutions. All of the resolutions are described explicitly. Our results suggest that the geometric framework of initial value spaces for the Painlevé equations extends to integrable PDEs. While not all the correspondences between the two frameworks are pursued in this thesis, they suggest tantalising rich directions for future research

Formation Types of Multiple Steerable 1-Trailer Mobile Robots Via Split-Rejoin Maneuvers

This paper considers the design of a motion planner that governs the motion of a flock of steerable 1-trailer nonholonomic robots, wherein each robot forms a three axle system. A set of artificial potential field functions is proposed for split/rejoin maneuvers of the flock within a constrained environment via a Lyapunov-based control scheme, essentially an artificial potential fields method, for the avoidance of obstacles and attraction to designated targets. The control scheme utilizes the artificial potential fields, within a leader-follower strategy, to accomplish desired formations and reformations of the flock. The effectiveness of the proposed nonlinear acceleration control laws is demonstrated through computer simulations of different formation shapes, namely, arrowhead, platoon, line, and column formations

Autonomous control of multiple mobile manipulators

This paper considers the autonomous navigation problem of multiple n-link nonholonomic mobile manipulators within an obstacle-ridden environment. We present a set of nonlinear acceleration controllers, derived from the Lyapunov-based control scheme, which generates collision-free trajectories of the mobile manipulators from initial configurations to final configurations in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulators with results through computer simulations of an interesting scenari

Formation types of a flock of 1-trailer mobile robots

In this paper, we control the motion of a flock of 1-trailer systems. A set of artificial potential field functions is proposed for split/rejoin of the flock of 1-trailer robots via the Lyapunov-based control scheme for the avoidance of obstacles and attraction to their designated targets. A leader follower strategy is used to accomplish the desired formation and reformation of the flock. The flock maintains a prescribed formation, splits and maneuvers around obstacles and then returns to its original position in the prescribed formation. The various formations shapes that we shall consider are the line, column, arrowhead and the double platoon. The effectiveness of the proposed control laws are demonstrated through computer simulations

Swarm navigation in a complex environment

This paper proposes a solution to the motion planning and control problem of car-like mobile robots which is required to move safely to a designated target in a priori known workspace cluttered with swarm of boids exhibiting collective emergent behaviors. A generalized algorithm for target convergence and swarm avoidance is proposed that will work for any number of swarms. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the proposed control laws are demonstrated via computer simulations of an emergent behavior

Tunnel passing maneuvers of a team of car - like robots in formation

The research essays the design of a motion planner that will simultaneously manage collision and obstacle avoidances of a team of nonholonomic car-like robots fixed in prescribed formation and ensure desirable tunnel passing maneuvers. This decentralized planner, derived from the Lyapunov-based control scheme works within a leader-follower framework to generate either split/rejoin or expansion/contraction of the formation, as feasible solutions to the tunnel passing problem. In either scenario, the prescribed formation will be re-established after the tunnel has been passed. Moreover, avoidance of the walls of a tunnel will be accomplished via the minimum distance technique. The results can be viewed as a significant contribution to the intelligent vehicle systems discipline