The primary goal of a mobile robot is to reach the desired goal by traversing an optimized path defined according to some criteria such as time, distance, and safety of the robot from any obstacles that may be in its way. Therefore, the backbone of autonomous mobile robots (AMRs) is path planning and avoiding obstacles. Many algorithms for path planning and obstacle avoidance have been presented by many researchers and each of these algorithms has several benefits and drawbacks. This paper focuses on comparing the performance of several metaheuristic algorithms that result in a more efficient, smoother, and shorter path for the mobile robot to reach the target in a complex environment. These algorithms include particle swarm optimization (PSO), chaotic particle swarm optimization (CPSO), modified chaotic particle swarm optimization (MCPSO), and firefly algorithm (FA). On the other hand, the paper proposes a hybrid algorithm by combining the FA and the MCPSO, namely the (HFAMCPSO). To demonstrate the effectiveness of the proposed algorithm in terms of the optimum cost function and obtaining the shortest path length, the optimal solution is compared to those of other path planning algorithms. Moreover, inverse dynamic and kinematic modeling are utilized to obtain the best torque and the best velocity actions for the wheels of the autonomous mobile robot. The proposed hybrid (FAMCPSO) algorithm provides enhancement on the path length equals (43.3%) and (25.5%) compared to the radial cell decomposition (RCD) and the A* algorithm, respectively. Moreover, the enhancement on the path length equals (2.3%) and (22.7%) compared to the firefly algorithm (FA) and the genetic algorithm (GA), respectively. All methods are simulated in an environment with static obstacles using the 2018b MATLAB package.