Range sensors and lidar

Web Serial needs desktop Chrome, Edge or Opera. Use a 3.3 V USB–serial adapter (CP2102, CH340, FT232): the sensor’s TX to the adapter’s RX, ground to ground, and 5 V to the sensor from USB.

The HC-SR04 sends eight cycles of 40 kHz after a 10 µs trigger, then holds ECHO high until the first echo arrives, so the distance is d = c·t/2. The speed of sound comes from the ideal gas, c = √(γ_RT_/M), with water vapour mixed in at the mole fraction h = RH·p_sat(T)/p (Buck’s saturation pressure), which lowers the molar mass and very slightly γ. That gives 343.2 m/s at 20 °C in dry air; 50 % humidity adds ≈ 0.6 m/s, matching the often-quoted c ≈ 331.4 + 0.606 T + 0.0124 RH.

The beam is traced as 121 rays across twice the datasheet half-angle, weighted by a Gaussian beam pattern whose −6 dB point is the half-angle. At 40 kHz (λ ≈ 8.6 mm) most hard surfaces are mirrors, so a ray returns only if it meets a surface within 10° of its normal; otherwise it reflects and is traced again (up to two bounces). Each returning ray’s strength is pattern × reflectance × cos⁴(incidence) / path² × air absorption (≈ 1.3 dB/m), echoes within 3 cm are merged, and the first group over a fixed threshold is the reading. It is a teaching model — real echoes also diffract around edges, and every module’s threshold and gain ramp differ — but it reproduces the things that catch people out: a thin pole only seen near the beam’s centre, a tilted wall that vanishes, soft furniture that reads through, and corridor ghosts.

The ToF model is approximate and says so on the page. Signal photons S = K·ρ·T/d² for a target that fills the cone, ambient counts A = K_a·E·T, and a target is reported while S/√(S + A) ≥ 5. K and K_a for each mode are fitted to two points from the datasheet: the maximum range on a white target in the dark, and under ST’s 200 kcps/SPAD ambient test (for the VL53L1X: short 136/135 cm, medium 290/76 cm, long 360/73 cm; for the TFmini-S: 12 m indoors and 7 m at 100 klux). It then predicts the trends: range ∝ √ρ (the long mode’s 1.6 m on 17 % grey against the datasheet’s 1.7 m), SNR ∝ √budget, and why the short mode is the one to use in a bright room. The VL53L1X field of view scales with the ROI side, 27° at 16 × 16 SPADs down to ≈ 15° at 4 × 4 (ST UM2555 and AN5191). The VL53L5CX grid casts one ray per zone across 45° × 45° and reports the perpendicular distance, as the ULD driver does.

The simulated lidar casts one ray per point against the room’s segments, boxes and circles, adds Gaussian range noise (1 cm, or 1 % of range for the RPLIDAR A1/A2), computes an intensity from reflectance, incidence angle and range, drops returns from black surfaces far away, and sees glass only within ≈ 14° of square-on. The occupancy grid is the log-odds inverse sensor model of Thrun, Burgard and Fox (Probabilistic Robotics, ch. 9): every cell a beam crosses gets −0.4, the end cell +0.85, clamped at ±4. The toy SLAM is scan-matching odometry: point-to-line ICP (Chen and Medioni, 1991; Censi’s PL-ICP, 2008) between consecutive scans — nearest neighbours from a hash grid, a shrinking outlier gate, the distance from each point to the line through its match and that match’s neighbours, linearised and solved as a 3 × 3 least-squares problem, starting from the last motion. (Plain point-to-point ICP, Besl and McKay 1992, lets the sparse points slide along walls and under-reads every turn by about a degree; it is in the engine as an option.) The increments are composed into a pose and the scans are mapped from it. With no loop closure it drifts, which is the point of showing the true path next to it.

The LD2410 frames follow HLK’s LD2410 serial communication protocol: commands FD FC FB FA, a length, a command word and value, 04 03 02 01, always between "enable configuration" (0x00FF) and "end configuration" (0x00FE); reports F4 F3 F2 F1, a length, the type (1 engineering, 2 basic), AA, the target state (0 none, 1 moving, 2 still, 3 both), moving distance and energy, still distance and energy, the detection distance, and in engineering mode the maximum gates and every gate’s moving and still energy — then 55 00 F8 F7 F6 F5. Engineering mode is command 0x0062, reading the parameters 0x0061, and a gate’s thresholds 0x0064 (gate 0xFFFF sets all). The LD2450 (its own HLK protocol document) reports AA FF 03 00, three targets of x, y (mm), speed (cm/s) and resolution, and 55 CC; x, y and speed are a 15-bit magnitude with the top bit set for a positive value. The simulator spreads a person’s movement and breathing energy over neighbouring gates with noise, and decides the state the way the module does, with each gate’s threshold and the "no-one" hold time.

The comparison figures are typical datasheet values; prices are rough bands. Check the datasheet of the exact part you buy — clone modules vary.