A tracked inspection robot is driven over a collapsed-building mock-up from a safe station. Built from a Blender 5.2 model; every number below comes from the equations in "The science".
Drive with the stick (or W A S D / arrow keys). Camera: Q / E. Arm: R / F. Grab: G. Relay: X. Move-and-wait: M.
Top bar: battery. Lower bar: stability margin (full = far from tipping, empty = about to roll over).
Margin = received power minus receiver sensitivity. Lines: line of sight, one wall, two walls. Dot: the robot now. Below 0 dB the video freezes and the robot stops (failsafe). Drop a relay at the door to bridge the dead zone.
The operator camera shows the world as it was one video-delay ago and your stick takes one command-delay to arrive. Try "Move+wait": short bursts, then stop and let the picture catch up.
This is a teaching model of remote driving a small tracked robot on a rescue / inspection task. It is not a model of any real vehicle, carries no payload other than a supply box, and has nothing to do with weapons. Numbers are textbook-level and chosen for clarity.
A tracked vehicle turns by driving the two tracks at different speeds. The ideal yaw rate is w = (vR - vL) / B, but the tracks must scrub sideways over the ground, so the real turn is slower. We use the standard effective track width chi x B, with chi between 1.15 (hard concrete) and 1.6 (loose sand). The scrub torque Mr = 0.9 mu N Lc / 4 must be supplied by the motors; on grippy ground the available torque limits the turn.
On a slope of angle a the drive force needed to hold or climb is m g sin a + Crr N, and the grip available is mu N with N = m g cos a. The robot stalls or slides when tan a > mu. The tracks and brakes are modelled with Coulomb friction: a sliding robot loses its grip and gains speed down the slope.
A vehicle rolls over a track edge when the ground-reaction friction force F acting at height h of the centre of gravity (CG) outweighs the restoring moment of the weight. Statically, on a side slope this gives the classic tip angle = atan((W/2) / h); nose-up / nose-down angles use the lever (Lc/2 +- x_cg). The CG height is computed from the hull, the arm (forward kinematics), the mast and the payload, so raising the arm or the mast, or carrying the kit high, lowers the tip angle. The same criterion is applied dynamically: turning at speed adds a lateral force m w v, so tipping occurs when (g sin b + w v) / (g cos b) > W / (2 h). Compare with the slide angle atan(mu): whichever angle is smaller happens first.
Free-space path loss from the Friis equation, then walls and fading:
Doubling the distance costs 6 dB. L_wall grows with frequency (6 dB at 433 MHz, about 16 dB at 2.4 GHz, 21 dB at 5.8 GHz: illustrative values for brick / concrete). Sensitivity depends on the video bit rate: about -94, -88 and -82 dBm for SD, HD and Full HD. A slow shadow-fading term of a few dB is added. Below roughly 12 dB margin the video frame rate and quality drop and packets are lost; at 0 dB the link fails and the robot's failsafe halts it. A relay adds one more hop; its margin is the smaller of the two hops minus 1 dB.
Driving by watching a delayed picture is a feedback loop with a time delay t. If the operator moves at a speed proportional to the distance still to go (gain K), the position error obeys e'(t) = -K e(t - t) once the vehicle's own lags are added. The loop is stable only for K below a critical gain; with a pure delay it is K_crit = pi / (2 t), and with a motor lag t1 and speed-loop lag t2 the limit follows from the phase condition w t + atan(t1 w) + atan(t2 w) = pi/2. Beyond it the robot oscillates with growing overshoot; below it the approach is smooth only if K t < 1/e. The practical cure is "move and wait": command a short move, stop, and look again after the round trip. It is slower but cannot overshoot.
Electrical power = base electronics (28 W) + radio transmit power / 0.25 + (thrust x track speed + turning scrub power) / 0.7. No regeneration is assumed. Climbing, soft ground, turning and heavy payload all cost energy; a short route on firm ground saves battery.
2-D motion on a height field with quasi-static tilt; no track-soil shear model, suspension, or terrain deformation; a single friction coefficient per surface; wall loss is a fixed dB per crossing and the antenna pattern is isotropic; video latency is a constant plus a link-quality term; human reaction time is a fixed 0.25 s in the lab trial. The robot is generic and unbranded; any resemblance to a product is coincidental.