Robot Arm Impedance-Control Safety Simulator

This simulator drives a real 2-link robot arm with impedance control instead of rigid position control: each joint's torque is computed as a virtual spring-damper, τ = K·(θ_target − θ) − D·θ̇, integrated frame by frame from real forward kinematics. Because the joints only ever feel a spring pulling toward the goal, the arm naturally complies when its end-effector contacts the obstacle, rather than driving through it at full force. A safety limiter continuously measures contact force and, when it crosses the configured threshold, genuinely reduces the effective stiffness so the arm backs off — the same power-and-force-limiting principle used on real collaborative robots. Tune stiffness and damping to compare a fast-but-dangerous high-impedance arm against a slow-but-safe low-impedance one, and toggle the limiter to see the difference between scripted safety and one whose numbers are actually a physical consequence of the control law.