Trajectory Planning in Articulated Robots Using the Lagrangian Dynamics Modelling Technique

Abstract

Accurate trajectory planning is still essential if articulated robots are to move with the precision, efficiency, and smoothness needed in busy or tightly packed work areas. In response, this study introduces a novel planning framework rooted in Lagrangian dynamics, using that theory to guide the creation of near-optimal paths for multi-joint robot systems. Because the approach is built on first principles, it can naturally include actuator limits, inertial coupling, and nonlinear contact forces, giving engineers a clear and workable picture of how a robot will behave in practice. The motion description is then shaped by combining these dynamic equations, obtained through the classic Euler-Lagrange method, with higher-level constraints expressed both in joint angles and in Cartesian space. Motivated by recent progress in optimization, the authors deploy a hybrid planner that balances time-jerk minimization with model-predictive control, thus accommodating tasks ranging from slow waypoint traversal to rapid equipment reconfiguration. Comprehensive experiments on simulated robotic arms and wheeled platforms show improvements of up to 30% in tracking precision and of 25% in energy consumption, even in the presence of hard nonlinear bounds. These results confirm that the Lagrangian approach can generate robust, real-time trajectories suitable for demanding industrial automation, surgical robotics, and autonomous space vehicles.