Considerate and Cooperative Model Predictive Control for Energy-Efficient Truck Platooning of Heterogeneous Fleets (2208.02119v1)

Published 3 Aug 2022 in eess.SY

Abstract: Connectivity-enabled automation of distributed control systems allow for better anticipation of system disturbances and better prediction of the effects of actuator limitations on individual agents when incorporating a model. Automated convoy of heavy-duty trucks in the form of platooning is one such application designed to maintain close gaps between trucks to exploit drafting benefits and improve fuel economy, and has traditionally been handled with classically-designed connected and adaptive cruise control (CACC). This paper is motivated by demonstrated limitations of such a control strategy, in which a classical CACC was unable to efficiently handle real-world road grade and velocity transient disturbances without the assistance of fleet operator intervention, and is non-adaptive to varied hardware and loading conditions of the operating truck. This automation strategy is addressed by forming a cooperative model predictive control (MPC) for eco-platooning that considers interactions with trailing trucks to incentivize platoon harmonization under road disturbances, velocity transients, and engine limitations, and further improves energy economy by reducing unnecessary engine effort. This is accomplished for each truck by sharing load, maximum engine power, transmission ratios, control states, and intended trajectories with its nearest neighbors. The performance of the considerate and cooperative strategy was demonstrated on a real-world driving scenario against a similar non-considerate control strategy, and overall it was found that the considerate strategy significantly improved harmonization between the platooned trucks in a real-time implementable manner.

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Summary

The paper introduces a cooperative MPC framework that overcomes CACC limitations in handling grade disturbances and heterogeneous powertrains.
It employs a distributed receding-horizon optimization that integrates real-time neighbor vehicle data to ensure consistent gap tracking and velocity harmonization.
Simulation results demonstrate significant fuel savings, enhanced platoon coherence, and reduced disengagements compared to anticipative MPC strategies.

Considerate and Cooperative Model Predictive Control for Heterogeneous Truck Platooning

Overview and Motivation

The paper addresses substantial limitations of classical Connected Adaptive Cruise Control (CACC) strategies in real-world, connectivity-enabled truck platoons. Traditionally, CACC controllers have demonstrated efficacy in managing highway platoons for homogeneous fleets on level terrain or within controlled environments. However, recent on-road experiments have exposed critical vulnerabilities under conditions of transient velocity, significant road grade, heterogeneous powertrains, and asynchronous gear states, where classical CACC underperforms, fails to maintain platoon coherence, or disengages. Notably, these deficiencies remain even in fleets composed of trucks with nominally identical hardware, underscoring the inadequacy of extant gap-tracking controllers for scalable, robust energy-optimal platooning.

To address these shortcomings, the authors propose a Considerate and Cooperative Model Predictive Control (MPC) framework. This approach explicitly shares heterogeneous truck parameters—load, engine power, transmission, state, and trajectory information—between neighboring vehicles. The result is a receding-horizon, distributed cooperative optimization leveraging bidirectional (and potentially multi-directional) information flows to harmonize control actions (see schematic (Figure 1)).

Figure 1: Bi-directional connected and cooperative heterogeneous truck platoon.

The cooperative MPC accommodates and anticipates the propulsive limitations of trailing vehicles, directly incorporating their predicted responses and limitations into the control problem of leading vehicles. This structure incentivizes the entire convoy towards actuation-constrained, harmonized platooning with a specifically eco-centric objective.

Limitations of Classical Automation and Problem Formulation

Empirically, the paper demonstrates the inability of CACC-enabled platoons to maintain safe and efficient spacing when subject to realistic grade disturbances and powertrain heterogeneity. Figure 2 in the paper (not shown here) illustrates the failure mode in which an automatically upshifted gear under road grade disables the following vehicle's ability to track the gap, ultimately leading to loss of platooning and CACC disengagement.

These observations drive the Constrained, Distributed, and Cooperative MPC formulation, whose design objectives are as follows:

Maintain dynamically feasible platoon gaps under realistic grade/load/gear disturbances.
Optimize joint engine effort subject to heterogeneous actuation limits and constraints.
Promote gap-tracking and velocity harmonization even in mixed-mass, mixed-powertrain, and mixed-gear configurations.
Robustify against leader breakaway/detachment through explicit consideration for trailing vehicles.

The modeling framework is high-fidelity and physics-based, featuring longitudinal dynamics, drag reduction modeling (via empirically derived inter-vehicle gap-dependent drag curves), engine/transmission constraints, powertrain lags, and finite road grade preview.

Cooperative Considerate MPC Architecture

The control architecture is distributed and scalable, with each truck $k$ solving a joint multi-agent dynamic optimization. Critically, each truck considers not only its own horizon and constraints but also a model of the trailing truck ( $k+1$ ), incorporating shared real-time state and constraint information (e.g., mass, gear, max engine power, desired gap).

The joint stage cost function includes:

penalization of total engine effort for both agent and follower,
gap tracking and velocity tracking with slack for feasibility,
soft compliance to neighbor-suggested control actions,
terminal cost on time-to-goal velocity.

Constraints are imposed for gap safety, velocity (non-negative, non-excess), actuation and engine power, and soft enforcements to avoid infeasibility from model mismatches or real-time preview uncertainty.

Each agent solves:

$\min_{U^{(k)}, U^{(k+1)}} J^{(k)} + J^{(k+1)}$

subject to joint nonlinear dynamics, nonlinear input/state constraints, and application of only the ego control.

Noteworthy is the capability for anticipatory variants ("A-MPC") with $q_\mathrm{compliance} = 0$ , yielding an anticipative but non-cooperative strategy often producing leader breakaway.

Numerical Results and Performance Analysis

Simulation studies were conducted over both synthetic and real-world road grade profiles, featuring 3-truck heterogeneous convoys with pronounced mass and powertrain variability. Several key findings emerged:

Platoon Coherence: The considerate (C-MPC) controller achieved uninterrupted gap maintenance across all studied scenarios, while anticipative (A-MPC) controllers frequently led to leader–follower detachment, platoon dissolution, and multiple control disengagements, especially under high grade and trailing truck underpower conditions.
Harmonization and Constraint Enforcement: C-MPC enabled velocity and gap synchronization between vehicles, explicitly constraining the leader to slow down in anticipation of trailing limitations—markedly evident on uphill segments. Figure 2 of the paper shows the leader adjusting speed to accommodate the follower’s power capability, maintaining feasible intervehicle gaps and preventing detachment.
Fuel Economy: The cooperative strategy resulted in a strong reduction of unnecessary acceleration/braking events, decreasing both transient engine effort and overall joint fuel consumption. The performance summary in Table 1—reproduced below—confirms statistically significant reductions in gap RMSE and disengagement instances.

Controller	Fuel [kg/100km]	Headway [s]	Gap RMSE [m]	Disengagement Rate
Considerate	5.16 (fwd)	0.72 (avg)	1.25	0
Anticipative	5.12 (fwd)	1.40 (avg)	276.7	0.5

C-MPC reduced fuel consumption over A-MPC by approximately 1.8% on average and eliminated disengagement events even in highly heterogeneous fleets.
Gap control RMSE for C-MPC was consistently low (1–5 m), while A-MPC saw values exceeding 200 m in certain breakaway scenarios.
Standard deviation trends empirically corroborate the robustness and predictability of the considerate method under varying permutations.

Comparative scenario sweeps across all permutations of $\{14,22,30,38\}$ t lead–follower–tailer loadings further emphasized the superior coherence and robustness of the considerate MPC.

(Figure 2)

Figure 2: Performance of the considerate MPC on the S-shaped grade route, demonstrating adaptive leader velocity reduction to ensure gap preservation under trailing truck actuation saturation.

(Figure 3)

Figure 3: Excerpt of US highway simulation; considerate MPC maintains small, steady gap error while anticipative MPC suffers major transient loss of platoon structure.

Systemic and Theoretical Implications

This work establishes that purely local, non-cooperative predictive controllers are inadequate for robust, scalable truck platooning in realistic and heterogeneous conditions. By internally modeling the neighbor's dynamics, anticipated control envelope, and incorporating explicit soft compliance to neighbor plans, considerate distributed MPC robustifies the entire convoy against both transient and persistent disturbances.

Key theoretical insights:

Joint dynamic constraints are essential: Modeling only ego dynamics and preview is insufficient when convoy agents can be underactuated or unpredictably perturbed.
Distributed bidirectional communication and optimization are necessary: Legislating leader compliance offers a mechanism for global robustness without resorting to centralized control, maintaining real-time feasibility and scalability.
Bidirectional cooperation incurs negligible fuel and performance penalties: Contrary to the expectation that leader constraint might "drag" convoy efficiency, the cooperative MPC demonstrated significant energy savings at the fleet level and eliminated costly disengagements.

Future Developments and Broader Impact

Integrating such considerate, cooperative MPC frameworks into autonomous fleet HMIs will make possible self-organizing platoons that are robust to fleet diversity and real-world uncertainty. Key next steps include:

Extension to larger heterogeneous fleets, exploring decentralized learning-based rollout strategies for scalability.
Real-time adaptation to unknown or dynamic follower models (e.g., when human-driven vehicles or additional cut-ins are present).
Incorporation of stochastic preview and model uncertainties, leveraging robust or adaptive MPC variants for higher-guarantee safety-critical deployment.
Exploration of convoy-level fuel credits and eco-credits for "considerate behavior" within transport networks, potentially incentivizing broader V2V data sharing and joint optimization.
Combination with online reinforcement learning controllers for adaptation in coordination with formal safety specifications.

Conclusion

The proposed distributed, considerate, and cooperative MPC solves the major limitation of classical CACC under real-world, heterogeneous conditions by enforcing convoy harmony through explicit neighbor-aware motion planning. Empirical results show dramatic improvements in convoy stability, gap synchronization, and robust fuel savings. The approach should be considered a new baseline for real-world deployable automation in heavy-duty truck platooning of mixed fleets.