Fourth-Order Runge-Kutta Method

In robot path planning, the Fourth-Order Runge-Kutta method serves as a widely adopted numerical algorithm for solving ordinary differential equations that govern motion dynamics. This algorithm enables robots to determine optimal movement trajectories toward target positions by iteratively calculating intermediate steps with high precision. In practical implementations, the Fourth-Order Runge-Kutta method facilitates path planning in complex environments through key computational steps: slope estimation at four intermediate points (k1-k4), weighted averaging of these slopes, and incremental position updates using a time-step parameter. Typical applications include logistics automation (e.g., transporting goods in factories) and medical assistance (e.g., delivering pharmaceuticals in hospitals). The core algorithm can be implemented using a function that calculates derivatives of the system's state variables, followed by iterative updates to the robot's position and velocity vectors. Research on optimizing this method—such as adaptive step-size control or parallelization—holds significant importance for advancing robotics technology, particularly in enhancing trajectory accuracy and computational efficiency.