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Cooperative look-ahead control for fuel-efficient and safe heavy-duty vehicle platooning

Valerio Turri, Bart Besselink, Karl H. Johansson

arXiv:1505.00447v1eess.SY

TL;DR

HDV platooning can reduce aerodynamic drag and emissions, but slopes make uncoordinated close-spacing trajectories inefficient or infeasible. The paper develops a two-layer architecture using preview-based platoon optimization and distributed real-time control, with simulations suggesting follower-vehicle fuel savings of up to 12% versus standard platoon controllers.

  • Problem

    Large HDV mass and limited engine power make slopes substantially affect feasible speed profiles, so maintaining short platoon spacing without coordination can produce inefficient or infeasible trajectories.

  • Method

    A two-layer architecture uses a platoon coordinator with dynamic programming and preview topography information, plus distributed model predictive control for real-time vehicle and spacing control.

  • Results

    Simulations of realistic scenarios suggest fuel savings of up to 12% for follower vehicles compared with standard platoon controllers.

  • Takeaways & Limitations

    The architecture coordinates platoon speed and spacing using road preview to target fuel-efficient and safe HDV platooning.

Abstract

from arXiv · show

The operation of groups of heavy-duty vehicles (HDVs) at a small inter-vehicular distance (known as platoon) allows to lower the overall aerodynamic drag and, therefore, to reduce fuel consumption and greenhouse gas emissions. However, due to the large mass and limited engine power of HDVs, slopes have a significant impact on the feasible and optimal speed profiles that each vehicle can and should follow. Therefore maintaining a short inter-vehicular distance as required by platooning without coordination between vehicles can often result in inefficient or even unfeasible trajectories. In this paper we propose a two-layer control architecture for HDV platooning aimed to safely and fuel-efficiently coordinate the vehicles in the platoon. Here, the layers are responsible for the inclusion of preview information on road topography and the real-time control of the vehicles, respectively. Within this architecture, dynamic programming is used to compute the fuel-optimal speed profile for the entire platoon and a distributed model predictive control framework is developed for the real-time control of the vehicles. The effectiveness of the proposed controller is analyzed by means of simulations of several realistic scenarios that suggest a possible fuel saving of up to 12% for the follower vehicles compared to the use of standard platoon controllers.

I. INTRODUCTION

HDV platooning can reduce fuel use and emissions, but road slopes and vehicle dynamics make uncoordinated close-spacing control inefficient or infeasible. The paper proposes a two-layer look-ahead architecture that combines platoon-level optimization with distributed real-time vehicle control.

  • Motivation: 29% of European Union CO2 emissions come from transport, with 11% directly attributable to road freight transportation.Globally, surface freight transport emissions are expected to increase up to 347% in 40 years if no measure is taken.
  • Motivation: Platooning reduces aerodynamic drag by operating HDVs at small inter-vehicular distances, with experiments reporting fuel-consumption reductions up to 7%.About one fourth of HDV fuel consumption is related to aerodynamic drag.
  • Motivation: HDV mass and limited engine power make slopes disrupt constant-speed operation, causing uphill power-limit violations or downhill braking and wasted energy.The paper motivates look-ahead control because altitude variations significantly affect longitudinal forces and fuel consumption.
  • Approach: The proposed architecture separates a platoon coordinator, which computes a preview-based fuel-optimal speed profile, from decentralized vehicle controllers that safely track it in real time.The coordinator uses dynamic programming, while the vehicle layer uses distributed model predictive control for speed and gap-policy tracking.
  • Motivating experiment: In a 45 km experiment, follower vehicles saved 4.1% and 6.5% overall, but the second vehicle consumed 4% more fuel than driving alone in the particularly hilly Sector A.The experiment involved three HDVs weighing 37.5, 38.4, and 39.5 tons; steep sections represented 23% of the road length.
  • Motivating experiment: Three motivating segments expose feedback-control limitations through undesired braking, large headway deviations, and switching between fueling and braking modes.The passages identify prediction and receding-horizon coordination as ways to anticipate vehicle behavior before critical gaps or actuator saturation occur.

B. Vehicle and platoon model

The paper models HDV longitudinal motion through powertrain, braking, gravity, rolling resistance, and distance-dependent aerodynamic forces. Its fuel model relates fuel flow to vehicle speed and traction force, then simplifies operation using an optimal-gear assumption and regression.

  • Vehicle dynamics: HDV longitudinal dynamics combine engine, braking, gravity, rolling-resistance, and aerodynamic-drag forces.Vehicle speed and position form the state, while engine and braking forces are control inputs.
  • Vehicle dynamics: Aerodynamic drag is modeled with a drag coefficient that depends on distance to the preceding vehicle.The dependence is fitted to experimental data, while the leading vehicle’s spacing-related drag reduction is neglected.
  • Fuel model: BSFC characterizes fuel consumed per generated energy across engine speed and torque operating points.The 400 hp engine map uses equal-power curves and identifies fuel-optimal operating points for different generated powers.
  • Fuel model: Fuel flow is expressed from vehicle speed, traction force, and gear ratio after assuming ideal power transfer through the transmission.The vehicle-speed relation uses engine speed and gearbox ratio under a no-slip assumption.
  • Fuel model: The controller fuel model removes gear-ratio dependence by assuming a continuously selectable, always-optimal gear ratio.The resulting optimal fuel-flow curve is linearly regressed, and its approximation error is reported as negligible.

IV. PLATOON CONTROLLER ARCHITECTURE

The architecture separates look-ahead platoon coordination from safety-critical real-time vehicle control. The coordinator optimizes a common space-based speed profile using route topography, while distributed vehicle controllers track it and maintain spacing.

  • Architecture: The system architecture comprises a mission planner, a platoon coordinator, and vehicle controllers.The mission planner proposes routes and platoon opportunities; the coordinator uses road information; vehicle controllers execute individual profiles.
  • Platoon coordinator: The platoon coordinator computes a fuel-optimal speed profile for the entire platoon using route topography, average-speed requirements, and all vehicle constraints.Its inputs include the mission planner’s average speed and current vehicle states, plus slope and speed-limit data.
  • Platoon coordinator: A single speed trajectory defined over road position allows every platoon vehicle to follow the same profile when spacing uses a pure time delay.The coordinator also specifies time gaps as the delay between consecutive vehicles passing the same point.
  • Platoon coordinator: The coordinator can operate receding-horizon dynamic programming with kilometer-scale preview and periodic profile updates.The DP formulation is characterized by spatial discretization, horizon length, and refresh frequency, and may recalculate after strong deviations.
  • Vehicle controllers: Distributed vehicle controllers perform safety-critical real-time tracking and use inter-vehicle communication to maintain the spacing strategy.The coordinator uses a nonlinear model for fuel prediction, whereas the vehicle layer uses a linear model for fast computation.

A. Platoon model

The platoon coordinator uses a space-discretized vehicle model to optimize speed, forces, and inter-vehicle distance while reducing computational complexity. This formulation approximates distance because its original definition cannot be expressed directly in the space domain.

  • A. Platoon model: The coordinator discretizes the vehicle model in space using an implicit Euler approximation.
  • A. Platoon model: The space-domain model represents speed, engine and braking forces, and distance to the preceding vehicle as functions of position.
  • A. Platoon model: Replacing the average-speed constraint with travel time in the cost removes time-dependent constraints and significantly reduces computational complexity.
  • A. Platoon model: Because distance cannot be defined directly in the space domain, the formulation uses an approximation based on the current vehicle speed.
  • A. Platoon model: The model constrains vehicle inputs and includes bounds on engine and braking forces.

2) State constraints:

The coordinator imposes speed and common-profile constraints and solves a dynamic-programming problem that trades off platoon fuel consumption against travel time. The vehicle-controller layer then tracks the resulting profile and gap policy through distributed MPC.

  • 2) State constraints:: The speed is bounded to account for road speed limits, while a common-speed constraint requires vehicles to follow the same profile.
  • 2) State constraints:: The common-profile constraint reduces dynamic-programming search from the number of vehicles to one dimension, enabling fast computation.
  • 2) State constraints:: The coordinator minimizes whole-platoon fuel consumption while maintaining a desired average speed through a weighted fuel-and-travel-time cost.
  • 2) State constraints:: The dynamic-programming problem optimizes the coordinator inputs over the horizon subject to its initial conditions.
  • 2) State constraints:: Each local vehicle controller receives the optimal speed profile and time gap, uses preceding-vehicle state information, and generates optimal trajectories for low-level control.
  • 2) State constraints:: The distributed MPC formulation is parameterized by discretization time, horizon length, refresh frequency, and prediction-horizon duration.

A. Vehicle model

Each vehicle MPC predicts speed, position, and acceleration trajectories, while reference and assumed trajectories connect local optimization to the coordinator’s profile and predecessor information. Input and speed constraints incorporate vehicle limits, safety needs, and fuel-efficient coasting.

  • A. Vehicle model: The MPC vehicle model uses predicted speed and position states together with acceleration as the control input.
  • A. Vehicle model: Optimal, reference, and assumed state trajectories are maintained alongside corresponding input trajectories.
  • A. Vehicle model: Reference trajectories are computed from the coordinator’s optimal speed profile and the vehicle’s current position.
  • A. Vehicle model: Assumed trajectories are computed from optimal and real vehicle trajectories and communicated to the following vehicle.
  • A. Vehicle model: Acceleration is constrained by nonlinear braking-force and engine-power limits, with external forces included in the constraint.
  • A. Vehicle model: A soft input constraint permits braking when safety is activated or when required by the platoon coordinator, while speed remains bounded by road limits.

C. Safety constraint

The safety design models predecessor acceleration as a disturbance and defines a robust controlled invariant set for adjacent vehicles. The result extends across the platoon and is implemented in MPC using safety constraints over the prediction horizon.

  • C. Safety constraint: The controller must handle deviations from predicted platoon behavior caused by internal disturbances or external traffic events.
  • C. Safety constraint: Safety is studied through continuous dynamics of adjacent vehicles, with follower acceleration as control input and predecessor acceleration as an exogenous disturbance.
  • C. Safety constraint: The admissible-state and input sets use conservative acceleration bounds determined under limits on speed, vehicle mass, and road slope.
  • C. Safety constraint: The safety set is defined by inequality constraints and is a robust controlled invariant set under admissible predecessor and follower inputs.
  • C. Safety constraint: The safety-set construction guarantees that a follower can respond to emergency braking so both adjacent vehicles stop without collision.
  • C. Safety constraint: In MPC, each follower computes its safety set using the assumed predecessor trajectory; horizon-wide constraints produce safe, smoother, and more fuel-efficient predicted trajectories.

D. Cost function

The vehicle-controller cost function balances trajectory tracking, gap-policy tracking, actuator excitation, and safety-constraint softening through weighted terms.

  • The cost function penalizes deviations in predicted state, acceleration, and a softening variable.These terms correspond to trajectory tracking, actuator-related behavior, and softened safety constraints.
  • The gap-policy contribution is weighted through ζ_i, which varies by vehicle position in the platoon.The supplied formulation assigns 0 to the first vehicle and ζ̄ to subsequent vehicles.
  • Weights Q, R, and ζ̄ tune the trade-off between reference tracking, gap-policy tracking, and actuator excitation.The parameters Q, R, and ζ̄ are constrained so that ζ̄ ∈ [0, 1].
  • The softening weight P is chosen large so that substantial braking is associated primarily with activation of the safety constraint.The safety constraint is fsafe(x_i(t_j+1|t_k)) ≥ 0.

E. Model predictive control formulation

The MPC problem uses state-dependent constraints and safety requirements to generate real-time vehicle-control actions, and can be recast as a QCQP for efficient solution.

  • The MPC optimization is evaluated over j = k, ..., k + H_MPC − 1 and includes an initial-condition constraint.The initial condition is represented by constraint (42h).
  • For implementation, state-dependent constraint sets are replaced by sets evaluated at predicted states.The replacements use A_i(x̂_i(t_j|t_k)), A_e,i(x̂_i(t_j|t_k)), and V(ŝ_i(t_j|t_k)).
  • Because the safety constraint is quadratic and convex, the MPC problem can be reformulated as a quadratic constraint quadratic programming problem.This reformulation enables use of efficient QCQP solvers.
  • The vehicle controller outputs the desired acceleration a*_i(t_k) from the optimal MPC input trajectory.It also outputs a boolean variable indicating whether the desired acceleration should be tracked by the BMS or EMS.

VII. PERFORMANCE ANALYSIS OF THE PLATOON

The performance analysis isolates the platoon coordinator by assuming exact tracking of high-level speed trajectories and spacing policies, then compares fuel-efficiency against standard controllers.

  • The analysis focuses on fuel-efficiency and compares the platoon coordinator with standard controller setups.The comparison is designed to assess the coordinator independently from the low-level vehicle-tracking strategy.
  • The simulations assume HDVs exactly follow the speed trajectories and spacing policies specified by the high-level controllers.This removes low-level tracking effects from the coordinator comparison.

A. Experiment setup

The experiments compare CC, LAC, and CLAC across gap policies, vehicle compositions, and a 45 km road, emphasizing energy use and braking on downhill sections. CLAC reduces follower energy and fuel use in the reported scenarios, although long downhill segments can still require braking.

  • Experiment setup: The benchmark uses two HDVs on a 45 km road and evaluates homogeneous and heterogeneous platoons using energy and fuel consumption.The heterogeneous cases vary vehicle masses between 35, 40, and 45 t while keeping the same powertrain.
  • Experiment setup: The compared control strategies are cruise control (CC), look-ahead control (LAC), and cooperative look-ahead control (CLAC).CC follows a reference speed, LAC uses road-slope preview for the first vehicle, and CLAC follows the platoon coordinator's profile.
  • Experiment setup: The gap policies are space gap, headway gap, and time gap; under TG, the follower may exceed theoretical maximum engine power and brake to maintain the prescribed gap.The energy bars are normalized to a single vehicle driving alone with CC and split into gravity, roll, drag, and braking components.
  • Fuel-efficiency results: 3.5% and 6.4% energy savings are obtained for the first and second vehicles, respectively, with LAC compared with CC.Switching from LAC to CLAC increases first-vehicle energy by 0.1% but decreases second-vehicle energy by 3.7%.
  • Fuel-efficiency results: 10.8% fuel savings occur with CLAC versus CC for a heavier follower, compared with 5.4% for a lighter follower.The reported CLAC normalized fuel consumption does not significantly change when vehicle order is reversed in the homogeneous case.
  • Downhill behavior: CLAC's savings primarily come from reducing braking energy downhill, and both HDVs can avoid braking in the described CLAC scenario.Longer downhill segments can still force braking because the lower speed bound prevents sufficient speed reduction beforehand.

C. Fuel-efficiency analysis for different gap policies

The analysis compares space, headway, and time gap policies under the same control strategy, showing that time gaps best accommodate varying road slopes and reduce energy use. Space gaps can force followers to brake or exceed power limits, while headway gaps provide an intermediate behavior.

  • Experimental setup: The comparison evaluates homogeneous 40 t platoons using space, headway, and time gaps with the same CC control strategy.Fuel is normalized against each vehicle driving alone with CC.
  • Gap-policy comparison: Space gaps require followers to match the leader’s speed over time, causing braking or power-limit violations when the leader enters an uphill.The follower may brake while still on flat road and later exceed the power limit to preserve the required gap.
  • Gap-policy comparison: Time gaps save more energy than space and headway gaps and allow vehicles to follow the same speed trajectory in space.This scaling property supports platoons with more vehicles.
  • Gap-policy comparison: Headway gaps trade off time-gap and space-gap behavior by allowing distance to decrease during uphill sections, but less rapidly than under time gaps.The same qualitative behavior applies to both synthetic-hill and original-road scenarios.

A. Safety analysis

The safety analysis shows that distributed vehicle controllers activate braking when measured spacing reaches the safety threshold, including under severe emergency braking. Integrated look-ahead coordination also produces smooth, fuel-efficient behavior across road slopes.

  • Safety analysis: Safety constraints activate follower braking when effective distance reaches the computed safety distance, with stronger leader braking triggering more follower responses.The tested decelerations were 1, 2, and 3 m/s^2 for 0.9 s at 5, 25, and 55 s; one, then both followers brake as the braking intensity increases.
  • Safety analysis: Emergency braking at 7 m/s^2 activates safety constraints in each controller and guarantees no collision between the vehicles.The leader brakes once briefly and later until reaching a full stop.
  • Integrated control: The integrated architecture makes all vehicles follow the same speed and distance profiles in space while followers generate less power because of reduced air drag.The result comes from the coordinated platoon coordinator and vehicle-controller layers.
  • Integrated control: On a steep downhill, the coordinator slightly fuels the leader so followers can coast, avoiding braking for all vehicles.On a longer downhill, it instead lowers speed, then combines leader coasting with slight follower braking to maximize efficiency.
  • Evaluation: The architecture is evaluated through numerical experiments that study the coordinator and vehicle-controller layers separately and together.The vehicle controller tracks the coordinator’s reference speed and generates real-time desired acceleration.
  • Scope boundary: The powertrain model assumes a continuously selectable gear ratio over an unlimited span, unlike typical commercial HDV gearboxes.Future work must address fixed ratios, gear-shift losses, and shift timing.
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