LbCS navigation controllers of Twining Lagrangian swarm individuals

Abstract

This paper presents stabilizing velocity controllers for the individuals of two Lagrangian swarms, which navigates from their initial configuration space to their final configuration space, ensuring intra and inter swarm individual collision avoidance. The motion of the individuals is based on Reynold's rules of separation, alignment, and cohesion. Using the three pillars (safety, shortest and smoothest path) of Lyapunov based control scheme (LbCS), the velocity controllers of the individuals of the two swarms are derived from multiple Lyapunov functions. The effectiveness of the controllers is validated through computer simulations.

Linear manipulator: Motion control of an n-link robotic arm mounted on a mobile slider

“…The proposed system has higher flexibility as it can move easily along the rail to perform assigned tasks. Its increased mobility offers better use of space and has the ability to contribute towards high productivity when compared to the anchored manipulators presented in [13] and [18] . The linear manipulator system presented in this study is a modification of existing robotic arms due to its ability to reposition and navigate to distant targets, resulting from a change in work requirements.…”

“…The ruling principle behind the potential method is to assign a repulsive field to each obstacle and an attractive field to the target [15] , [53] . The Lyapunov function is the sum of each and every repulsive and attractive potential functions [54] , [48] , thus establishing a basis for deriving the controllers of a linear manipulator. The repulsive potential function is a ratio of a positive tuning parameter to the obstacle avoidance function.…”

“…As described in [13] , a robotic arm is an open or closed kinematic chain of rigid links interconnected by movable joints; the two commonly used being revolute and prismatic. Robotic arms are traditionally mounted to rigid structures as they perform specific tasks in constrained work environments.…”

“…This modification of the robotic arm concept and the two-step switch movement enables the linear slider to extend the arm's workspace by advancing linearly along the rail towards an elusive target with increased reachability. In comparison, the anchored robotic arm systems mentioned in [13] , [30] , [18] offer a restricted workspace and minimal operational functionalities of the end-effector in performing designated tasks. The proposed unanchored linear manipulator can have real-world applications in industrial sectors requiring process repeatability tasks like material handling and pick-and-place.…”

Switch controllers of an n-link revolute manipulator with a prismatic end-effector for landmark navigation

“… Sharma, Vanualailai & Prasad (2017) proposed the Lyapunov-based Control Scheme (LbCS), which falls under the artificial potential field method, widely used in robotics research for motion planning and control of robotic systems. The time-invariant nonlinear velocity or acceleration controllers can be derived from LbCS, which has been successfully applied in the literature to find feasible and stabilizing solutions to a variety of problems ( Sharma, Vanualailai & Singh, 2015 ; Sharma, Vanualailai & Singh, 2014 ; Kumar, Vanualailai & Sharma, 2016 ; Chand, Kumar & Chand, 2021 ; Sharma et al, 2018 ; Kumar et al, 2021 ; Sharma, Raj & Vanualailai, 2018 ).…”