## 1 Introduction  
In the last few decades, humans have started looking towards greater mobility in the tasks that machines perform. Since that era, researchers have been getting involved in the development of telepresence robots (TRs) [1; 2; 3; 4]. MERLIN (Mobile Experimental Robot for Locomotion and Intelligent Navigation) was developed on the same idea of mobility. In the modern era, human-robot interaction is increasing and demanding in many application areas, including healthcare systems and military applications. This is due to the advancement and capability of robots to perform complex tasks in dangerous and prohibited environments. The evolution of the digital era and smart robotic designs are continuously simplifying daily routine tasks with fast response and precision. Researchers are working very hard to design such robots, but still, the robots have many limitations in performing various functions. On the other hand, it has become necessary for humans to involve robots in tasks from remote locations or in harmful situations, e.g., COVID-19. Robots can execute these schedules tasks instead of human beings, who can instead sit in remote locations [1; 2; 3; 4]. Mobile robots are also extensively used in other applications, such as entertainment, audio-video communication, and remote monitoring. However, the design of many physical parameters--including the maneuverability, controllability, and stability of human-robot interaction--still needs attention [5]. Telepresence robots (TRs) have the facility of a video conferencing display to keep in contact with the robot continuously. The application of TRs is found in many areas, including remote offices [2; 3; 4; 5], online education for disabled students [6; 7], and shopping plazas [8]. The employment of TRs is not easy, even though a continuous social presence receives attention daily [5; 8; 9]. In hazardous or remote locations, precise navigation to avoid obstacles is another challenge, limited due to the camera image resolution [10; 11]. To overcome these challenges, researchers work day and night on control mechanisms. The robot is controlled using the remote controller, which is connected to the device and communicates through the remote location. Although the use of robots is still increasing, the stability of the control systems should be designed appropriately so that the journey will be free of collision [12]. Keeping in mind the development and application of robots in [12; 13; 14; 15], we developed a speed control method with additional sensors, which can provide information to control the robot's speed by detecting obstacles and determining another safe path. Such a useful design for robots, which controls the fast and slow motion of the robot through a dense and narrow passage, is currently in demand. Much work has been conducted previously in developing the industrial robots reported in [16; 17; 18]. However, to the best of our knowledge, distance-based speed control has not yet been developed. This motivated us to design a controller for deploying robots in healthcare and military systems. The main contribution of this paper is to analyze the trajectory and stabilize the nonlinear behavior by designing optimized control system algorithms. This paper presents and illustrates some ideas that could contribute to the genetic basis of the architecture, allowing us to consider the previous requirements as much as possible. The idea of the proposed work was to design such a robot that can plan to accomplish the specified tasks. To fulfill this requirement, the focus of the current research was on the devising of trajectory planning and driving new algorithms. Then, experimental verification was performed to determine the accuracy of the algorithms, along with noise analysis. A chassis of an HPI Savage 2.1 monster truck was developed to carry out the experimental work, as shown in Figure 1. The vehicle was equipped with Ackermann steering, with a four-wheel drive capacity. The force is propagated on all four wheels in the same direction.