A quaternion-based, transmission-scheduled multi-IMU system for low-cost lower-limb joint-angle measurement: bench validation against an encoder up to the Cardan singularity, and wireless protocol benchmarking

Wearable inertial measurement unit (IMU) networks are an affordable alternative to optical motion capture for lower-limb measurement in sport, physical activity, and rehabilitation outside the laboratory, but two problems limit their kinematic signal: the reference-frame dependence of joint angles formed by differencing Euler angles from separate sensors, and frame-level desynchronisation caused by unscheduled wireless transmission. We developed and evaluated a four-node wireless IMU system addressing both. Joint angles were computed from the relative orientation quaternion between adjacent segments. This removes the dependence on a common global heading, but a singularity re-enters when an angle sequence is extracted, and here the reported joint angle is itself that singular rotation, reaching 88.4 deg in magnitude at end-range. Transport was reorganised as a deterministic, master-driven slotted protocol over ESP-NOW: a hardware-timer broadcast trigger carried a shared sequence number and timestamp, each node replied after a fixed per-node slot delay of 1.2 + 2.5k ms, and serialisation was moved out of the receive callback. Joint-angle accuracy was validated on a mechanical rig against a 600 pulses-per-revolution encoder; no human data were collected. Communication was benchmarked over paired 300 s recordings of the proposed protocol and a queue-based baseline. Against the encoder, root-mean-square error was 1.12, 0.79, and 0.86 deg for the three IMU pairs, with a bias of +0.70, +0.52, and +0.46 deg and 95% limits of agreement no wider than 3.4 deg. Cross-correlation placed the end-to-end latency at 44 ms; compensating for it left the bias unchanged and halved the standard deviation of the difference. Relative to the baseline, the proposed protocol raised the complete-frame rate from 97.20% to 99.99% while increasing the trigger rate from 20 to 50 Hz, cut duplicate packets from 16.13% to 0.31%, and reduced median per-second latency jitter from 26.5–35.5 ms to 3.4–4.9 ms. Scheduling, however, acts on transmission, not acquisition: the nodes sample on free-running loops, and their acquisition instants within a frame differed by a median of 9.0 ms. The transport layer is therefore deterministic and the bench estimation chain accurate, while acquisition-time skew limits joint-angle measurement during fast movement.