In the context of industrial automation, optimising automated guided vehicle (AGV) trajectories is crucial for enhancing operational efficiency and safety. They must travel in crowded work areas and cross narrow corridors with strict safety and time requirements. Bio-inspired optimization algorithms have emerged as a promising approach to deal with complex optimization scenarios. Thus, this paper explores the ability of three novel bio-inspired algorithms: the Bat Algorithm (BA), the Whale Optimization Algorithm (WOA) and the Gazelle Optimization Algorithm (GOA); to optimise the AGV path planning in complex environments. To do it, a new optimization strategy is described: the AGV trajectory is based on clothoid curves and a specialised piece-wise fitness function which prioritises safety and efficiency is designed. Simulation experiments were conducted across different occupancy maps to evaluate the performance of each algorithm. WOA demonstrates faster optimization providing suitable safety solutions 4 times faster than GOA. Meanwhile, GOA gives solutions with better safety metrics but demands more computational time. The study highlights the potential of bio-inspired approaches for AGV trajectory optimisation and suggests avenues for future research, including hybrid algorithm development.