Impedance Control — Phase Portrait & Force-Displacement (2D)

A wrist-mounted force/torque sensor is the difference between a robot arm that can pick up an egg and one that crushes it. This 2D companion to the robot-arm impedance-control simulator drops the 3D arm animation and instead plots the controller's own virtual mass-spring-damper dynamics directly: a live phase portrait of position error versus velocity, and a force-versus-penetration diagram tracing how the sensed contact force settles onto the series-spring prediction F_ss = K·k_env/(K+k_env)·d. Tune the controller's commanded stiffness and damping, choose how soft or rigid the surface is, and press to watch the trajectory spiral into equilibrium (or ring, if damping is too low) while the joint torques update live via the same manipulator Jacobian, τ = J^TF, used by real torque-controlled joints.