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Robotic arms play an indispensable role in multiple sectors such as manufacturing, transportation and healthcare to improve human livelihoods and make possible their endeavors and innovations, which further enhance the quality of our lives. This paper considers such a robotic arm comprised of n revolute links and a prismatic end-effector, where the articulated arm is anchored in a restricted workspace. A new set of stabilizing switched velocity-based continuous controllers was derived using the Lyapunov-based Control Scheme (LbCS) from the category of classical approaches where switching of these nonlinear controllers is invoked by a new rule. The switched controllers enable the end-effector of the robotic arm to navigate autonomously via a series of landmarks, known as hierarchal landmarks, and finally converge to its equilibrium state. The interaction of the inherent attributes of LbCS that are the safeness, shortness and smoothness of paths for motion planning bring about cost and time efficiency of the controllers. The stability of the switched system was proven using Branicky’s stability criteria for switched systems based on multiple Lyapunov functions and was numerically validated using the RK4 method (Runge–Kutta method). Finally, computer simulation results are presented to show the effectiveness of the continuous time-invariant velocity-based controllers.

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.

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