Speed & Separation Monitoring in 2D: ISO/TS 15066 Cobot Safety Envelope

Human Worker

Approach speed v_h 1.2 m/s

SSM Controller (ISO/TS 15066)

System reaction time T_r 0.15 s

Robot braking decel. a_r 4.0 m/s²

Robot max speed v_max 0.8 m/s

Live Readouts

● FULL SPEED

Separation D

— m

Required S_p

— m

Allowed v_r

— m/s

Speed override

100%

How it works

Speed and Separation Monitoring (SSM) is one of the four collaborative operating modes defined in ISO/TS 15066 for industrial cobots. Instead of a fixed safety cage, the controller continuously computes the minimum protective separation distance S_p required between the human and the robot for the robot's current commanded speed, and never lets the robot move faster than the speed that keeps the measured separation D at or above S_p:

S_p(v_r) = v_h·T_r + v_r·T_r + v_r² / (2·a_r) + C

v_h  human approach speed (default 1.2 m/s here)
T_r  system reaction/reset time (sensing + processing delay)
v_r  robot's current commanded speed
a_r  robot's braking deceleration once a stop is triggered
C    fixed intrusion distance (how far a limb reaches before detection)

Because S_p grows with v_r (linearly from the reaction-time term, quadratically from the stopping-distance term), the controller inverts the formula every frame: given the live measured separation D, it solves the quadratic a·v_r² + b·v_r + c = 0 (with a = 1/(2a_r), b = T_r, c = v_hT_r + C − D) for the largest non-negative root, clamped to [0, v_max]. That solved value is the commanded speed the arm actually moves at.

Drag the human marker on the floor plan to set the live separation instantly — the arm's speed reacts in real time, exactly like a lidar/ToF-tracked worker.
v_h / Walk toward / away — sets the assumed worst-case approach speed and starts an automatic radial walk.
T_r — a slower sensor/control loop demands more standoff distance even at the same speed.
a_r — weaker brakes (small a_r) blow up the v_r²/(2a_r) term, shrinking the safe speed fast.
v_max — the ceiling the controller is allowed to command when nobody is nearby.

Real deployments use this exact calculation with lidar or 3D time-of-flight cameras tracking worker position at 20–50 Hz, re-solving S_p every cycle — it is the mathematical basis for cobots like the Universal Robots UR-series and KUKA LBR iiwa running SSM-mode line-side, without any fixed fence.

Robot arm (SSM-throttled) Human worker (drag me) Protective separation S_p

drag the worker to set separation

Speed and Separation Monitoring in 2D: ISO/TS 15066 Cobot Safety Envelope