In this paper, we present a novel approach for Proportional–Integral–Derivative (PID) tuning of a robotic manipulator, modeled using the Lagrange method and validated through comprehensive modeling and simulation. To optimize the PID gains, we developed a hybrid algorithm that combines Greylag Goose Optimization (GGO) with the Sine Cosine Algorithm (SCA), leveraging the strengths of both optimization techniques. The proposed hybrid algorithm, termed GGOSCA, was tested against GGO and Particle Swarm Optimization (PSO) using three objective functions: Lyapunov Based Function (LBF), Integral of Absolute Error (IAE), and Integral of Time-weighted Absolute Error (ITAE). The results demonstrated that GGOSCA outperforms both GGO and PSO across all objective functions. Specifically, GGOSCA achieved the lowest costs of 0.1018, 0.2484, and 0.6601 for LBF, IAE, and ITAE, respectively, compared to 0.1022, 0.2580, and 0.6939 for GGO, and 0.1023, 0.2660, and 0.7273 for PSO. The superior performance of GGOSCA highlights its effectiveness in balancing exploration and exploitation, making it well-suited for complex control tasks such as PID tuning in robotic systems. This novel combination of GGO and SCA provides a robust and efficient solution for optimizing control parameters in dynamic environments, demonstrating its potential through rigorous modeling and simulation.

This paper develops a closed-form dynamic model of the planar multi-link flexible manipulator. The structural flexibility in the links is modeled using Rayleigh beam theory with clamped-mass boundary conditions. The solution of the Rayleigh beam equation is provided using the assumed mode method. The dynamic equations of motion are derived using the Lagrangian formulation. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The time-domain simulation results and analysis of the dynamic model are presented to show the effect of the payload on the mode shapes and frequencies and the dynamics of the system.

Hybrid robots incorporate the advantages of both aerial-only and terrestrial-only vehicles to achieve enhanced mobility and better energy efficiency. Among hybrid vehicles, spherical robots offer the best maneuverability. While operating on uneven surfaces is one of the main benefits of spherical robots, the current literature only covers control of these robots on flat surfaces. This work presents two control algorithms to track a desired trajectory and angular velocity of spherical robots on uneven terrains. The proposed control algorithms can be used when the terrain is known analytically or empirically (i.e., point cloud). By allowing the controller to use empirical information about the terrain profile, this work broadens the implementation of spherical robots in real applications.

Spherical robots are typically comprised of an actuation unit enclosed by a spherical shell. Among nonholonomic systems, spherical robots offer the best maneuverability and lowest energy consumption (due to their omnidirectional movement and single contact point with the ground). This allows them to traverse rough and uneven terrains. Further, using their ability to roll on the ground, they can provide a significantly higher operating time compared to aerial-only robots. Unfortunately, these robots are under-emphasized by researchers compared to other robots (i.e., legged or wheeled robots). Additionally, despite their potential to be used in a multitude of real-world applications, spherical robots have not been successfully adopted by the industry. This is due to the lack of controllability and traversability of the developed designs. In this paper, we introduce a hybrid rolling/flying robot. This design benefits from a flywheel to reduce the effects of the terrain (shocks and vibrations) on the camera and sensors. Our design allows the application of existing control algorithms of drones (such as PX4) on a rolling system. In addition, we propose a dynamics model that can use the point cloud representation of the terrain to simulate the motion of the system with applications in real-time modeling and control.