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

A car - like mobile manipulator with an n - link Prismatic Arm

In this research, the Lyapunov based Control Scheme (LbCS) is used to solve the motion planning and control problem of a car-like mobile robot with a long extendible prismatic arm comprising n∈N links. The prismatic arm consists of a base revolute joint and n∈N translational joints, and is mounted on the wheeled car-like mobile platform. The kinematic model of the manipulator is developed, and velocity based algorithms are utilized to firstly, move the car-like base from an initial position to its pseudo-target and secondly, maneuver the end-effector to its designated target, taking into account the restrictions and limitations of the prismatic links and the steering control laws of the system. Computer simulations are presented to illustrate the effectiveness of the proposed control laws

Herding predators using swarm intelligence

Swarm intelligence, a nature-inspired concept that includes multiplicity, stochasticity, randomness, and messiness is emergent in most real-life problem-solving. The concept of swarming can be integrated with herding predators in an ecological system. This paper presents the development of stabilizing velocity-based controllers for a Lagrangian swarm of n∈N individuals, which are supposed to capture a moving target (intruder). The controllers are developed from a Lyapunov function, total potentials, designed via Lyapunov-based control scheme (LbCS) falling under the classical approach of artificial potential fields method. The interplay of the three central pillars of LbCS, which are safety, shortness, and smoothest course for motion planning, results in cost and time effectiveness and efficiency of velocity controllers. Computer simulations illustrate the effectiveness of control laws

Obstacle Avoidance Problem for Second Degree Nonholonomic Systems

In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consideration satisfies controllability conditions with iterated Lie brackets up to the second order. The time-varying control strategy is defined explicitly in terms of the gradient of a potential function. It is shown that the limit behavior of the closed-loop system is characterized by the set of critical points of the potential function. The proposed control design method can be used under rather general assumptions on potential functions, and particular applications with navigation functions are illustrated by numerical examples.Comment: This is the author's accepted version of the paper to appear in: 2018 IEEE Conference on Decision and Control (CDC), (c) IEE

Lyapunov - based controllers of an n - link Prismatic Robot Arm

This research provides a generalized stabilizing velocity controllers for planer robot arm with a base rotational joint and n∈N translation joint for navigation. The end-effector of the planer robot arm has to navigate from an initial to a final configuration space in an environment, which cluttered with obstacles. The velocity controllers are developed from a Lyapunov function, total potentials, designed via Lyapunov-based control scheme (LbCS) falling under the classical approach of artificial potential fields method. The effectiveness of the controllers is validated through computer simulations

A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact

This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is derived in terms of contravariant vectors, rolling velocity, and geometric invariants, including normal curvature, geodesic curvature, and geodesic torsion of the respective contact curve. The equation is represented with geometric invariants. It can be readily generalized to suit both arbitrary parametric surface and contact trajectory and can be differentiated to any order. Effect of the relative curvatures and torsion on spin-rolling kinematics is explicitly presented. The translation velocity of an arbitrary point on the moving object is also derived based on the Darboux frame

Lane changing and merging maneuvers of car-like robots

This research paper designs a unique motion planner of multiple platoons of nonholonomic car-like robots as a feasible solution to the lane changing/merging maneuvers. The decentralized planner with a leaderless approach and a path-guidance principle derived from the Lyapunov-based control scheme generates collision free avoidance and safe merging maneuvers from multiple lanes to a single lane by deploying a split/merge strategy. The fixed obstacles are the markings and boundaries of the road lanes, while the moving obstacles are the robots themselves. Real and virtual road lane markings and the boundaries of road lanes are incorporated into a workspace to achieve the desired formation and configuration of the robots. Convergence of the robots to goal configurations and the repulsion of the robots from specified obstacles are achieved by suitable attractive and repulsive potential field functions, respectively. The results can be viewed as a significant contribution to the avoidance algorithm of the intelligent vehicle systems (IVS). Computer simulations highlight the effectiveness of the split/merge strategy and the acceleration-based controllers

Motion control of an articulated mobile manipulator in 3D using the Lyapunov - based control scheme

Finding feasible solutions to motion planning and control problem of robotic systems in different environments with various applications is an active area of research. This article presents a new solution to the motion planning and control problem of a three-dimensional articulated mobile manipulator comprising a car-like mobile platform and a three-dimensional n-link articulated arm using the Lyapunov-based control scheme. The motion of the system is described as twofold: first, the car-like mobile platform moves from an initial position to its pseudo-target, and second, when the mobile platform is within some predefined distance from the pseudo-target, the end-effector of the robot arm is attracted to its designated target. Therefore, presenting a new 2-Step Algorithm in this paper for dual movement of the articulated mobile manipulator in 3D. In addition, a workspace cluttered with fixed spherical and rod obstacles of random sizes and positions is considered in this research. For the mobile manipulator to avoid an obstacle, the Minimum Distance Technique is adapted where a point on the robot that is closest to an obstacle will avoid the obstacle. The convergence of the two bodies and the stability of the mechanical system are guaranteed by the Lyapunov's direct method. The continuous nonlinear control laws proposed from the control scheme also take into account all mechanical singularities and velocity limitations associated with the system. Theoretical proofs and computer simulations validate the new continuous, acceleration-based, nonlinear, time-invariant control laws