Simulation of Industrial Robot Course Design

Industrial robot course design simulations typically involve implementing key algorithms for robot kinematics and dynamics, with Lagrangian formulation and Jacobian matrix methods being two core approaches. These methods not only help students master the theoretical foundation of robot control but also visually demonstrate the relationship between joint movements and end-effector trajectories through simulation. In code implementation, these algorithms are often structured as modular functions calculating transformation matrices and dynamic parameters.

In course designs, Lagrangian formulation is primarily used for robot dynamic modeling. By establishing system kinetic and potential energy expressions, it derives the relationship between joint torques and motion states. This method is suitable for analyzing dynamic characteristics of multi-degree-of-freedom robots, such as torque requirements during acceleration, deceleration, or load variations. Students must consider the effects of robot inertia matrix, Coriolis forces, and gravity. During simulation, they can observe torque variation curves for each joint along trajectories. Code implementation typically involves symbolic computation of energy equations and numerical differentiation.

The Jacobian matrix method focuses on kinematic analysis, establishing the mapping relationship between joint velocities and end-effector velocities. By computing the Jacobian matrix, it enables not only forward kinematics simulation but also velocity control and singularity analysis in inverse kinematics. Course designs often require students to complete robot trajectory planning based on Jacobian methods, such as linear or circular path tracking, while analyzing singular configurations when the matrix determinant becomes zero. Implementation commonly uses matrix inversion techniques and singularity avoidance algorithms.

Simulation programs usually integrate both methods, combined with visualization tools like MATLAB Robotics Toolbox or ROS to display robot motion processes. By adjusting parameters such as link lengths, joint limits, or payload mass, students can verify algorithm robustness and understand differences between theoretical models and actual control. Such course designs not only consolidate the mathematical foundation of robotics but also cultivate problem-solving capabilities for complex engineering challenges. Typical code structures include main simulation loops with real-time visualization callbacks.