In this paper, trajectory planning and navigation control problems have been addressed for a mobile robot. To achieve the objective of the research, an adaptive PSO (Particle Swarm Optimization) motion algorithm is developed using a penalty-based methodology. To deliver the best or collision-free position to the robot, fitness values of the all-random-positioned particles are compared at the same time during the target search action. By comparing the fitness values, the robot occupies the best position in the search space till it reaches the target. The new work integrated with conventional PSO is varying a velocity event that plays a vital role during the position acquisition (continuous change in position during the obstacle negotiation with the communication through random-positioned particles). The obstacle-negotiating angle and positional velocity of the robot are considered as input parameters of the controller whereas the robot's best position according to the target position is considered as the output of the controller. Simulation results are presented through the MATLAB environment. To validate simulation results, real-time experiments have been conducted in a similar workspace. The results of the adaptive PSO technique are also compared with the results of the existing navigational techniques. Improvements in results between the proposed navigation technique and existing navigation techniques are found to be 4.66% and 11.30%, respectively.