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Optimizing the Driving Profile for Vehicle Mass Estimation

Le Wang, Jessica Ye, Michael Refors, Oscar Flärdh, Håkan Hjalmarsson

TL;DR

The paper addresses accurate real-time mass estimation for autonomous heavy-duty vehicles operating in unstructured environments by proposing an application-oriented input design (AOID) framework that proactively designs informative driving profiles under physical constraints. It combines a Newtonian longitudinal model, non-causal Wiener filtering with Empirical Bayes parameter estimation for accelerometer signals, and LS mass estimation, then couples these with SDP- and branch-and-bound–based AOID formulations to realize minimum-time, minimum-distance, and maximum-accuracy driving profiles. Theoretical insights describe feasibility conditions and structural patterns of optimal inputs, while numerical and real-world tests on a Scania truck with two payloads validate the approach and show improved mass estimation accuracy without dedicated calibration runs. The work also introduces a non-causal Wiener filter to avoid phase lag, enhancing real-time estimation in practice and illustrating the practical impact for safer and more efficient autonomy in mining-like operations.

Abstract

Accurate mass estimation is essential for the safe and efficient operation of autonomous heavy-duty vehicles, particularly during transportation missions in unstructured environments such as mining sites, where vehicle mass can vary significantly due to loading and unloading. While prior work has recognized the importance of acceleration profiles for estimation accuracy, the systematic design of driving profiles during transport has not been thoroughly investigated. This paper presents a framework for designing driving profiles to support accurate mass estimation. Based on application-oriented input design, it aims to meet a user-defined accuracy constraint under three optimization objectives: minimum-time, minimum-distance, and maximum accuracy (within a fixed time). It allows time- and distance-dependent bounds on acceleration and velocity, and is based on a Newtonian vehicle dynamics model with actuator dynamics. The optimal profiles are obtained by solving concave optimization problems using a branch-and-bound method, with alternative rank-constrained and semi-definite relaxations also discussed. Theoretical analysis provides insights into the optimal profiles, including feasibility conditions, key ratios between velocity and acceleration bounds, and trade-offs between time- and distance-optimal solutions. The framework is validated through simulations and real-world experiments on a Scania truck with different payloads. Results show that the designed profiles are feasible and effective, enabling accurate mass estimation as part of normal transportation operations without requiring dedicated calibration runs. An additional contribution is a non-causal Wiener filter, with parameters estimated via the Empirical Bayes method, used to filter the accelerometer signal with no phase-lag.

Optimizing the Driving Profile for Vehicle Mass Estimation

TL;DR

The paper addresses accurate real-time mass estimation for autonomous heavy-duty vehicles operating in unstructured environments by proposing an application-oriented input design (AOID) framework that proactively designs informative driving profiles under physical constraints. It combines a Newtonian longitudinal model, non-causal Wiener filtering with Empirical Bayes parameter estimation for accelerometer signals, and LS mass estimation, then couples these with SDP- and branch-and-bound–based AOID formulations to realize minimum-time, minimum-distance, and maximum-accuracy driving profiles. Theoretical insights describe feasibility conditions and structural patterns of optimal inputs, while numerical and real-world tests on a Scania truck with two payloads validate the approach and show improved mass estimation accuracy without dedicated calibration runs. The work also introduces a non-causal Wiener filter to avoid phase lag, enhancing real-time estimation in practice and illustrating the practical impact for safer and more efficient autonomy in mining-like operations.

Abstract

Accurate mass estimation is essential for the safe and efficient operation of autonomous heavy-duty vehicles, particularly during transportation missions in unstructured environments such as mining sites, where vehicle mass can vary significantly due to loading and unloading. While prior work has recognized the importance of acceleration profiles for estimation accuracy, the systematic design of driving profiles during transport has not been thoroughly investigated. This paper presents a framework for designing driving profiles to support accurate mass estimation. Based on application-oriented input design, it aims to meet a user-defined accuracy constraint under three optimization objectives: minimum-time, minimum-distance, and maximum accuracy (within a fixed time). It allows time- and distance-dependent bounds on acceleration and velocity, and is based on a Newtonian vehicle dynamics model with actuator dynamics. The optimal profiles are obtained by solving concave optimization problems using a branch-and-bound method, with alternative rank-constrained and semi-definite relaxations also discussed. Theoretical analysis provides insights into the optimal profiles, including feasibility conditions, key ratios between velocity and acceleration bounds, and trade-offs between time- and distance-optimal solutions. The framework is validated through simulations and real-world experiments on a Scania truck with different payloads. Results show that the designed profiles are feasible and effective, enabling accurate mass estimation as part of normal transportation operations without requiring dedicated calibration runs. An additional contribution is a non-causal Wiener filter, with parameters estimated via the Empirical Bayes method, used to filter the accelerometer signal with no phase-lag.

Paper Structure

This paper contains 49 sections, 3 theorems, 82 equations, 40 figures.

Table of Contents

  1. Introduction
  2. Longitudinal Vehicle Dynamics Model
  3. Pretreatment of signals and Mass Estimation
  4. Non-causal Wiener filtering of noisy signals
  5. Estimating filter parameters
  6. Realization of the Wiener filter
  7. Real-data illustration
  8. Mass estimation
  9. Real-world illustration
  10. Application-oriented input design
  11. Application-oriented model quality constraints
  12. Experimental constraints
  13. Experimental cost
  14. Optimal input design formulations
  15. AOID for mass estimation in vehicles
  16. ...and 34 more sections

Key Result

Theorem 1

Assume the system starts from initial velocity $v_{\min}$. Let acceleration be bounded by $a_k \in [a_{\min}, a_{\max}]$, where $a_{\min} < 0 < a_{\max}$. Define Noting that $T_s$ is sufficiently small, we assume that $n_+$ and $n_{-}$ are integers.: Let $N = M(n_+ + n_-)$ where $M$ is the number of periods, and define the periodic acceleration pattern: Then:

Figures (40)

  • Figure 1: Normal driving velocity profiles of four trials for the used truck when the mass is $15$ tons.
  • Figure 2: Evolution of the mass estimate using velocity trajectories from Fig. \ref{['250625figure30']}.
  • Figure 3: Longitudinal forces on the vehicle.
  • Figure 5: LS estimates of the mass using different regressors.
  • Figure 6: Schematic of the observed time-optimal structure.
  • ...and 35 more figures

Theorems & Definitions (7)

  • Theorem 1: Sufficient condition for feasibility via periodic acceleration
  • Remark 1
  • Theorem 2: Critical Ratio for Distance Minimization
  • Theorem 3: Monotonic Amplification of the Travel Distance Gap with Respect to Velocity Range
  • proof
  • proof
  • proof