Industrial Kinematic Trajectory Model (IKTM): Coordinate-Free Autoregressive Generator

Max Amiri; David Eyers

cs.LGAug 27, 2026

Industrial Kinematic Trajectory Model (IKTM): Coordinate-Free Autoregressive Generator

Authors: Max Amiri, David Eyers

Organizations: School of Computing University of Otago Dunedin, New Zealand

Abstract

Mobility simulation supports logistics, safety, and communications planning in industrial environments such as ports, mines, and airports. Existing trajectory models, however, rely on absolute coordinates, road-network tokens, or semantic zones: representations that are site-specific and not well suited to unstructured industrial terrain. We introduce the Industrial Kinematic Trajectory Model (IKTM), a coordinate-free trajectory generator that represents industrial vehicle motion through kinematic sequences (speed and heading change) with no absolute spatial reference. IKTM uses an autoregressive causal transformer with probabilistic mixture heads and extends our prior coordinate-free Markovian model with deep sequence modelling and an explicit duration-conditioning signal. Trained on one site and evaluated zero-shot on three unseen sites, it matches the small-turn shape of the empirical turn-rate distributions of held-out telematics; across all four sites, the per-site mean Jensen-Shannon divergence over 100 sampling seeds spans approximately 0.035-0.050 bits under an oracle-length duration-target protocol and approximately 0.032-0.042 bits under a fully zero-shot prior-length protocol, with similar ranges whether out-of-distribution (OOD) duration targets are drawn from each held-out site's empirical length distribution or from the Site A prior. Both protocols stay above the metric's sampling-noise floor (<=0.0049 bits). Paired by site, the oracle-length values are 5.3-6.0x lower than those of a re-implementation of our prior Markovian model under the same 1 Hz protocol. Termination is duration-conditioned rather than spatial: rollouts stop on 100% of trials with a length-tracking error of +0.0 +/- 0.0 s against the sampled target (100 of 100 exactly on target; N=100, T=0.2, untouched in-distribution test split).

Figures & tables

Model	Domain	Coord.-free	Prob. output	Industrial
MobilityGPT [ 1 ]	Urban/Human	×	×	×
MoveGPT [ 2 ]	Urban/Human	×	×	×
TrajFM [ 4 ]	Urban/Vehicle	×	×	×
UniTraj [ 3 ]	Urban/Vehicle	×	×	×
TrajTok [ 5 ]	Urban/Vehicle	×	×	×
TrajGDM [ 11 ]	Urban/Human	×	✓	×

TABLE I: Qualitative Comparison of Trajectory Generation Models

Panel of Figure 2 — Fig. 1: IKTM trajectory preprocessing pipeline.

	Site A	Site B	Site C	Site D
Devices	450	130	164	125
Trips	179,151	13,749	21,503	23,844
1 Hz samples	19,600,183	1,720,760	2,547,585	2,204,640
Speed p95 (m/s)	10.00	6.94	11.72	8.89
Duration p95 (s)	311	439	380	251
Turn-rate p95 (deg/s)	50.37	41.32	47.79	56.50

TABLE II: Per-Site Dataset Statistics and Fleet Composition

Model	Speed	Heading	Stop	Stop
	RMSE	RMSE	BCE	Prec / Rec
	(m/s)	(deg)
Det. Transformer	0.16	21.6 ∘	0.0017	0.953 / 0.999
Prob. Transformer	0.15	22.7 ∘	0.0036	0.913 / 0.999
Det.+Dur. Transformer	0.13	19.8 ∘	$0.0000^{\dagger}$	$\mathbf{1.000/1.000}^{\dagger}$
IKTM (Prob.+Dur.)	0.12	21.3 ∘	$0.0003^{\dagger}$	$0.992/1.000^{\dagger}$

TABLE III: Next-Step Prediction Metrics: Site A Test Split (In-Distribution)

$\tau$ source	Speed	Heading	Stop	Stop
	RMSE	RMSE	BCE	Prec / Rec
	(m/s)	(deg)
Oracle (true $\tau$ )	0.12	21.3 ∘	0.0003	0.992 / 1.000
Prior (fixed, const.)	0.20	22.9 ∘	0.0624	0.685 / 0.005
None (ceiling, const.)	0.19	22.7 ∘	0.0690	0.963 / 0.002

TABLE IV:

\tau

-Control Ablation: IKTM, Site A Test Split, Teacher-Forced

Site	Speed	Heading	Stop	Stop
	RMSE	RMSE	BCE	Prec / Rec
	(m/s)	(deg)
Site A (ID-test)	0.12	21.3 ∘	0.0003	0.992 / 1.000
Site B (OOD)	0.13	19.6 ∘	0.0002	0.992 / 1.000
Site C (OOD)	0.14	20.7 ∘	0.0002	0.992 / 1.000
Site D (OOD)	0.15	23.5 ∘	0.0003	0.992 / 1.000

TABLE V: Cross-Site Next-Step Metrics: IKTM (Site A In-Distribution (ID), Sites B–D Zero-Shot OOD)

Train $\downarrow$ / Test $\rightarrow$	Site A	Site B	Site C	Site D
Site A	0.118 ∗	0.128	0.141	0.151
Site B	0.133	0.140 ∗	0.147	0.150
Site C	0.130	0.119	0.134 ∗	0.144
Site D	0.125	0.148	0.165	0.163 ∗

TABLE VI: Leave-One-Site-Out Speed RMSE (m/s),

4\times 4

Home-vs-Cross-Site Matrix

Fig. 2: An illustrative rollout from the full IKTM at

T=0.2

(left) alongside its speed and heading-change profile (right). The black circle marks the BOS start, the black

\times

the end-of-sequence (EOS) stop event.

		Oracle-length arm		Prior-length arm
Site	Type	Trip-len	Turn-rate	Trip-len	Turn-rate
		JSD (bits)	JSD (bits)	JSD (bits)	JSD (bits)
Site A	ID-test	0.061	0.039	0.061	0.039
Site B	OOD	0.047	0.057	0.081	0.044
Site C	OOD	0.049	0.031	0.060	0.027
Site D	OOD	0.024	0.033	0.039	0.036

TABLE VII: Generative Rollout Quality: IKTM (

N=100

Rollouts per Site, Canonical Seed 42)

	Site A	Site B	Site C	Site D
Noise floor (mean, 95% bootstrap interval)	0.0016 [0.0008,0.0034]	0.0014 [0.0007,0.0033]	0.0019 [0.0007,0.0049]	0.0017 [0.0009,0.0034]
i.i.d. marginal	0.0006	0.0007	0.0009	0.0011
Persistence (zero-turn)	0.245	0.211	0.287	0.275
Prior Markov [ 6 ]	0.231	0.267	0.202	0.197
IKTM trained on linear interp. (Section III-C )	0.233	0.198	0.274	0.256
IKTM (ours) , 100-seed mean	0.039	0.050	0.036	0.035

TABLE VIII: Turn-Rate JSD Baselines (Matched Protocol,

N=100

, Seed 42 Unless Noted)

Sign-change rate between consecutive nonzero $\Delta\theta$ steps
	Site A	Site B	Site C	Site D
Real	0.201	0.176	0.194	0.201
i.i.d. marginal	0.502	0.494	0.504	0.507
IKTM	0.162	0.158	0.169	0.163
Per-second acceleration exceeding 3 m/s 2 (% of steps)
Real	0.008	0.004	0.004	0.008

TABLE IX: Temporal Structure Under a Matched Protocol (

N=100

, Seed 42)

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University of Southern California

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