In many space exploration missions, where precise trajectory control is essential for successful operations, space robotics plays a critical role. This paper uses bond graph modeling to describe the dynamics of the system and to efficiently apply control schemes. This modeling method provides a strong framework for examining the behaviour and interactions of systems. Although bond graph modeling and Proportional-Integral-Derivative (PID) control are frequently combined, PID controllers frequently perform less than optimally in complicated or nonlinear systems. The controller parameters are optimized using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to get over this restriction. GA simulates the process of natural selection and evolution while, PSO a population-based optimization method, imitates the behaviour of a swarm. The goal of both algorithms is to determine the PID parameters in order to reduce trajectory errors and improve efficiency. This study presents an enhanced capability for redundant space robots to manage their trajectory during contacts with free-floating objects by merging PID with PSO and GA respectively.