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The PID control algorithm for balancing robot attitude control suffers from the problem of difficult parameter tuning. Previous studies have proposed using metaheuristic algorithms to tune the PID parameters. However, traditional metaheuristic algorithms are subject to the criticism of premature convergence and the possibility of falling into local optimum solutions. Therefore, the present paper proposes a CFHBA-PID algorithm for balancing robot Dual-loop PID attitude control based on Honey Badger Algorithm (HBA) and CF-ITAE. On the one hand, HBA maintains a sufficiently large population diversity throughout the search process and employs a dynamic search strategy for balanced exploration and exploitation, effectively avoiding the problems of classical intelligent optimization algorithms and serving as a global search. On the other hand, a novel complementary factor (CF) is proposed to complement integrated time absolute error (ITAE) with the overshoot amount, resulting in a new rectification indicator CF-ITAE, which balances the overshoot amount and the response time during parameter tuning. Using balancing robot as the experimental object, HBA-PID is compared with AOA-PID, WOA-PID, and PSO-PID, and the results demonstrate that HBA-PID outperforms the other three algorithms in terms of overshoot amount, stabilization time, ITAE, and convergence speed, proving that the algorithm combining HBA with PID is better than the existing mainstream algorithms. The comparative experiments using CF prove that CFHBA-PID is able to effectively control the overshoot amount in attitude control. In conclusion, the CFHBA-PID algorithm has great control and significant results when applied to the balancing robot. [ABSTRACT FROM AUTHOR]

• The path planning and path smoothing are combined through the high-order continuous Bezier curve. • An improved QPSO that incorporates two search mechanisms from bald eagle search (BES) is proposed. • The concept of semi-randomization is infused in some of our modifications in BES-MQPSO. • Enhanced intensive exploitation is performed by incorporating BES search and swoop mechanisms. • It may be the first time to apply BES tricks to help to enhance QPSO and into the path planning field. The design of path planning algorithms to obtain a smooth path that satisfies constraints such as obstacle avoidance, minimized cost, and dynamic feasibility for mobile robots in the workspace is a hot issue in the field of intelligent robotics. The metaheuristic optimization algorithm, which aims to solve path planning problems, is more efficient compared to traditional algorithms. In the current metaheuristic approaches, avoiding local minimum traps is the core goal of the scheme. In this paper, with the benefit of a high-order continuous Bezier curve, we construct an optimization problem of smooth path planning based on the length and the requirement of collision-free safety as constraints of the robot's expected path. Then, the smooth path planning problem is transformed into an optimization problem that searches the locations of control nodes of the Bezier curve. We solve the constructed path planning problem with our modified quantum particle swarm optimization algorithm (QPSO). Specifically, to overcome the shortcomings of the current PSO and QPSO-based particle swarm algorithms like prematurity, unbalanced global search, local exploitation, and local minima, we implement an improved QPSO algorithm denoted as BES-MQPSO that incorporates the search and swoop mechanisms from bald eagle search (BES) strategies. The method consists of four improved modifications: an improved local attractor, improved feature length, BES-enhanced intensive exploitation Strategy, and random variation mechanism. Our proposed BES-MQPSO with these four modifications is tested with benchmark functions and then applied to the smooth path planning problem. Finally, the superiority of BES-MQPSO is confirmed, and the ideal smooth path of the mobile robot is successfully planned. The planned path length is reduced by 4.45% and 2.82% compared to e-QPSO and SDEQPSO respectively, while the standard deviation is reduced by 67.46% and 69.82%, respectively. [ABSTRACT FROM AUTHOR]