On-Road Energy: Models, Optimization, and Infrastructure

• On-road energy is defined as the integrated process of modeling, estimating, optimizing, and managing vehicle energy consumption and transfer using physics-based and control methods.
• Methodologies span force decomposition, gradient-based trajectory optimization, and convex relaxations to achieve improved eco-driving performance and fuel efficiency.
• Infrastructure strategies include dynamic wireless charging, road electrification, and mobile energy storage to enhance energy exchange and reduce carbon emissions.

On-road energy denotes the modeling, estimation, optimization, delivery, and system-level management of energy consumed or transferred while vehicles move on road networks. In the cited literature, the term spans longitudinal resistance modeling, battery and fuel consumption estimation, regenerative braking, eco-driving trajectory planning, energy-aware routing, road electrification, dynamic wireless charging, vehicle-to-grid coordination, mobile energy storage, and carbon-emission estimation from transportation demand and network structure (Tian et al., 2024, Ahmadi et al., 2024, Ayaz et al., 2023, Llanes-Estrada et al., 2010). The topic is intrinsically multiscale: it begins with force and power balance at the vehicle level, extends to optimal control and pathfinding, and reaches infrastructure and grid coordination when energy is exchanged on-road rather than only at stationary charging facilities.

1. Physical and mathematical foundations

Most on-road energy models in this corpus start from the same longitudinal resistance decomposition. A representative formulation writes rolling resistance, aerodynamic drag, and gravitational load as

$$F_{\mathrm{roll}}(v,\theta)=C_r\,m\,g\,\cos\theta,\qquad F_{\mathrm{aero}}(v)=\tfrac12\,\rho\,C_d\,A\,v^2,\qquad F_{\mathrm{slope}}(\theta)=m\,g\,\sin\theta,$$

so that

$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$

and cumulative mechanical energy over a horizon is

$E=\int_0^T P(v(t),\theta(t))\,dt.$

Because this power expression is analytic in $v$ and $\theta$, it can be embedded directly in gradient-based trajectory optimizers (Tian et al., 2024).

Electric-vehicle path-planning models typically augment that decomposition with auxiliary loads and regeneration. One formulation decomposes total link cost into rolling resistance, aerodynamic drag, gravitational work, auxiliary power $P_{\mathrm{aux}}$, and a negative regeneration term on downhill links,

$$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$

with regeneration modeled as a fraction $\eta_{\mathrm{regen}}$ of downhill gravitational energy (Ahmadi et al., 2024). A related EV consumption model writes wheel power as the sum of inertial, rolling, drag, and grade components, followed by drivetrain and motor efficiencies and bidirectional treatment of regenerative braking in the battery-energy integral (Hadjigeorgiou et al., 5 Jun 2025).

Fuel-oriented autonomous-driving models further distinguish wheel power from fuel-rate. In "EMATO: Energy-Model-Aware Trajectory Optimization for Autonomous Driving" (Tian et al., 2024), the wheel force includes rolling resistance, aerodynamic drag, slope, and inertial force $M a_t$. The resulting wheel torque and engine operating point are mapped through interpolated engine maps, and the fuel-rate is then approximated by a smooth polynomial surrogate,

$$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$

On both a light-duty truck and a sedan, this fit achieves over $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$0 prediction accuracy (Tian et al., 2024).

A distinct line of work emphasizes reduced, physics-like models derived from high-fidelity simulators and then validated against chassis-dynamometer data. "Validation and Calibration of Energy Models with Real Vehicle Data from Chassis Dynamometer Experiments" (Carpio et al., 27 Mar 2025) constructs a simplified fuel-rate model with inputs limited to speed $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$1, acceleration $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$2, and road grade $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$3,

$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$4

After calibration of an Autonomie Mid-SUV template to a 2020 Toyota RAV4, the simplified model attains cumulative fuel error of $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$5 on HWFET, $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$6 on WLTC, and $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$7 on US06, while requiring negligible runtime $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$8 per time-step on modern CPU) (Carpio et al., 27 Mar 2025). This establishes a useful boundary in the literature: compact models can be sufficiently accurate for optimization and traffic-scale simulation if the reference model is itself well calibrated.

The corpus also shows that purely longitudinal models can be incomplete. In scaled experiments on an RC vehicle designed to match dimensionless groups of a full-scale EV, lateral maneuvers increased energy demand by about $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$9 to $E=\int_0^T P(v(t),\theta(t))\,dt.$0 per lane change under UDDS-like conditions, motivating an added term

$E=\int_0^T P(v(t),\theta(t))\,dt.$1

in EV energy models (Kumari et al., 20 May 2025). A plausible implication is that urban and winding-road estimators that ignore lateral dynamics may misstate range even when their longitudinal force balance is accurate.

2. Trajectory planning, optimal control, and eco-driving

On-road energy enters trajectory planning most directly when the objective function includes a differentiable fuel or energy model rather than only acceleration or jerk penalties. "Slope Considered Online Nonlinear Trajectory Planning with Differential Energy Model for Autonomous Driving" (Tian et al., 2024) formulates an online nonlinear program with decision variables $E=\int_0^T P(v(t),\theta(t))\,dt.$2, $E=\int_0^T P(v(t),\theta(t))\,dt.$3, traction acceleration $E=\int_0^T P(v(t),\theta(t))\,dt.$4, driver-oriented acceleration $E=\int_0^T P(v(t),\theta(t))\,dt.$5, and braking acceleration $E=\int_0^T P(v(t),\theta(t))\,dt.$6. Its objective combines leading-vehicle speed tracking, comfort regularization, and a model-aware fuel term based on the fitted fuel-rate polynomial $E=\int_0^T P(v(t),\theta(t))\,dt.$7. The constraints include kinematics, slope-dependent dynamics, hard ACC safety bounds, and box limits. In a receding-horizon implementation with a $E=\int_0^T P(v(t),\theta(t))\,dt.$8 horizon and $E=\int_0^T P(v(t),\theta(t))\,dt.$9, the direct NLP solves in approximately $v$0–$v$1 on PC and approximately $v$2 on embedded Xavier, which corresponds to roughly $v$3 update. Across $v$4 driving cycles and $v$5 slope profiles, the method improves fuel efficiency by $v$6 for a $v$7 sedan and $v$8 for a $v$9 diesel truck relative to a model-agnostic QP baseline, with speed losses of $\theta$0 and $\theta$1, respectively (Tian et al., 2024).

EMATO pushes the same principle into Frenet-frame motion planning. It begins with quintic longitudinal and lateral polynomials, then re-optimizes the timing and velocity profile through a CasADi-plus-IPOPT nonlinear program whose cost combines speed tracking, acceleration, braking, jerk, and fuel-per-distance (Tian et al., 2024). On an Intel i7 desktop, the solver converges in approximately $\theta$2; on an NVIDIA Xavier, in approximately $\theta$3. The reported gains depend strongly on how tightly end-state and comfort constraints are imposed. In adaptive-cruise-control studies, EMATO-B yields $\theta$4 miles-per-gallon improvement for a truck on flat roads and $\theta$5 for a sedan on flat roads, while relaxed variants reach up to $\theta$6 and $\theta$7 in truck-flat settings. In a $\theta$8 flat-road case at desired $\theta$9, EMATO generates a pulse-and-glide profile that reduces fuel consumption from $P_{\mathrm{aux}}$0 for constant cruising to $P_{\mathrm{aux}}$1 with no time loss (Tian et al., 2024).

Several works isolate specific eco-driving primitives. "Optimizing Energy-Efficient Braking Trajectories with Anticipatory Road Data for Automated Vehicles" (Prado et al., 2024) models three modes—disengaged coasting, engaged coasting, and active braking—and solves a switched optimal control problem using necessary conditions from the Hybrid Minimum Principle. The same paper also proposes a parametric approximation in four variables, $P_{\mathrm{aux}}$2, solved as a small nonlinear program. In the reported scenario $P_{\mathrm{aux}}$3 in $P_{\mathrm{aux}}$4, the indirect and direct methods differ by less than $P_{\mathrm{aux}}$5 in objective value, supporting the use of low-dimensional surrogates for real-time implementation (Prado et al., 2024).

"Energy Consumption Optimization for Autonomous Vehicles via Positive Control Input Minimization" (Hadjigeorgiou et al., 5 Jun 2025) argues that classical surrogates such as $P_{\mathrm{aux}}$6 penalize positive and negative accelerations symmetrically and therefore misrepresent actual energy usage. Its proposed metric,

$P_{\mathrm{aux}}$7

penalizes only energy-consuming control action. The resulting ECO+ formulation is convex; after piecewise-affine approximation of quadratic resistive forces, it becomes a linear program. The reported piecewise-affine approximation has objective error below $P_{\mathrm{aux}}$8 on average and a speed-up of approximately $P_{\mathrm{aux}}$9. In a $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$0 unsignalized-intersection scenario, ECO+ solves in an average of $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$1, compared with approximately $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$2 for the DC baseline and approximately $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$3 for a nonlinear solver in the KMMK case (Hadjigeorgiou et al., 5 Jun 2025).

Continuous-time optimal control also appears in "Optimal Racing of an Energy-Limited Vehicle" (Moehle, 2023), where the state includes position $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$4, speed $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$5, kinetic energy $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$6, and internal energy $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$7, and the engine loss map is modeled as $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$8. The paper shows that a simple convex relaxation of the nonconvex optimal control problem is tight, then solves the discretized problem with CVXPY and ECOS on a $$E_{\mathrm{total}}=E_{\mathrm{rr}}+E_{\mathrm{drag}}+E_{\mathrm{grade}}+E_{\mathrm{aux}}-E_{\mathrm{regen}},$$9-point grid. The resulting Pareto front makes explicit the nonlinear trade-off between travel time and energy: shorter travel times require disproportionately more energy, while modest increases in trip time yield large energy savings (Moehle, 2023).

Experimental validation of eco-driving controllers is comparatively rare in this literature. "Energy and Flow Effects of Optimal Automated Driving in Mixed Traffic: Vehicle-in-the-Loop Experimental Results" (Ard et al., 2020) uses a vehicle-in-the-loop architecture combining real vehicles, VISSIM traffic, ROS-based MPC, and calibrated OBD-II energy measurement. The reported outcome is up to $\eta_{\mathrm{regen}}$0 improved energy economy for both a gasoline Mazda CX-7 and a Nissan Leaf relative to calibrated human-like car-following, with no collisions in more than $\eta_{\mathrm{regen}}$1 of mixed-traffic runs and network throughput improvement of approximately $\eta_{\mathrm{regen}}$2 in strings with $\eta_{\mathrm{regen}}$3 penetration (Ard et al., 2020).

3. Routing, pathfinding, and energy-aware network optimization

At the route level, on-road energy becomes a path cost assigned to road segments or graph edges. Wu et al., in "Eco-Routing Navigation System for Electric Vehicles" (Wu et al., 2020), combine CONSULT III Plus data from a 2013 Nissan Leaf with GPS-based map matching and link-level polynomial calibration. For each road segment, the energy cost is $\eta_{\mathrm{regen}}$4, and Dijkstra’s algorithm is used to compute the least-energy path. On an independent Riverside Plaza dataset, the mean trip-level error is $\eta_{\mathrm{regen}}$5, speed measurements agree to SMAPE below $\eta_{\mathrm{regen}}$6, and archived-traffic simulations over $\eta_{\mathrm{regen}}$7 virtual trips show $\eta_{\mathrm{regen}}$8–$\eta_{\mathrm{regen}}$9 lower energy use than shortest-distance routing and $M a_t$0–$M a_t$1 lower energy use than shortest-time routing (Wu et al., 2020).

A broader generalization is the vehicle-specific cost model in "Vehicle Powertrain Connected Route Optimization for Conventional, Hybrid and Plug-in Electric Vehicles" (Qiao et al., 2016). There the trip cost is

$M a_t$2

with segment cost computed from fuel and electricity prices, average link speed, and link-by-link battery-state evolution. The reported least-cost path differs from the shortest-distance path for $M a_t$3 of $M a_t$4 origin-destination pairs for conventional vehicles and for $M a_t$5 of trips on average for electrified vehicles. On changed-route trips, the cost reduction averages $M a_t$6 and reaches $M a_t$7 for conventional vehicles; for electrified vehicles it averages $M a_t$8 and reaches $M a_t$9 (Qiao et al., 2016). For plug-in hybrids, route choice also depends on initial SOC: in a PHEV20, reducing initial SOC from $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$0 to $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$1 changes $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$2 of routes, and reducing it to $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$3 changes $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$4 (Qiao et al., 2016).

Large-scale EV pathfinding must additionally handle negative edge costs caused by regenerative braking. "Real-Time Energy-Optimal Path Planning for Electric Vehicles" (Ahmadi et al., 2024) writes each edge cost as the sum of rolling resistance, aerodynamic drag, gravitational work, auxiliaries, and regeneration, then introduces node potentials $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$5 so that reduced costs

$$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$6

remain nonnegative. The paper gives both a model-based reduction and a model-independent potential-energy reduction based on $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$7, both with $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$8 overhead per edge and no preprocessing. This permits Dijkstra-style real-time search even when some physical edges are energy-negative (Ahmadi et al., 2024).

When the initial battery level is unknown, the problem becomes a profile search rather than a single-source shortest path. "A Fast Heuristic Search Approach for Energy-Optimal Profile Routing for Electric Vehicles" (Ahmadi et al., 1 Dec 2025) computes a piecewise-linear profile $$\hat f_r(v,a_t)=o_0+o_1v+o_2v^2+o_3v^3+o_4v^4+(c_0+c_1v+c_2v^2)a_t.$$9 for all feasible initial energies. It replaces profile-merging label-correcting methods with a label-setting multi-objective A* search that stores only a compact summary $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$00 and prunes labels using a profile dominance rule. On ten real-world road networks from the 9th DIMACS Challenge, enriched with SRTM elevation and a Nissan Leaf $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$01 consumption model, the unidirectional profile variants run within $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$02 of plain A* while supporting full profile queries, and the paper reports $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$03–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$04 speedups over prior label-correcting profile A* methods (Ahmadi et al., 1 Dec 2025).

For fleets rather than single vehicles, energy-aware routing can incorporate time-dependent speeds, acceleration, and payload. "Energy-Efficient Routing for Electric Vehicles under Acceleration and Load Effects" (Su et al., 23 Nov 2025) defines instantaneous power as

$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$05

replacing step-function traffic models by piecewise linear velocity profiles over each arc. The corresponding ALD-EVRP is solved either by BonMin or by a custom LNS-SPP meta-heuristic. On $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$06 Singapore instances, the LNS-SPP method solves all instances within $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$07 each and yields up to $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$08 additional savings when full load dynamics are accounted for; the reported comparisons also show that ignoring real-time load underestimates energy consumption, whereas using only the initial payload overestimates it (Su et al., 23 Nov 2025).

4. On-road charging, electrified infrastructure, and mobile energy exchange

A different branch of the literature treats on-road energy not as a quantity to be minimized but as a quantity that can be delivered, exchanged, or scheduled while vehicles are moving. The earliest paper in this set, Llanes-Estrada and Waidelich’s "Left lane road electrification" (Llanes-Estrada et al., 2010), proposes overhead catenary electrification of only the leftmost motorway lane. The design uses an underground $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$09 AC feeder, substations every approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$10 converting to approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$11 DC, an overhead contact conductor around $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$12 above the pavement, and a vehicle-mounted pantograph-like collector. The target power is $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$13 per vehicle, corresponding to $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$14 vehicles per kilometer $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$15 per electrified lane-kilometer. In the Madrid study, the authors estimate that on-road charging could reduce a $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$16–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$17 battery for $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$18 range to a $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$19–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$20 pack for buffering, saving approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$21 and approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$22 in battery cost. The reported infrastructure capital cost is approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$23, with annual maintenance of approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$24 of capex and a break-even traffic intensity of approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$25 EV-km/day (Llanes-Estrada et al., 2010).

Recent work explores wireless rather than conductive delivery. "Electric Road Systems for Smart Cities: A Scalable Infrastructure Framework for Dynamic Wireless Charging" (Agnihotri et al., 14 Dec 2025) describes modular inductive charging coils embedded in $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$26–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$27 pavement segments spaced every $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$28, driven at $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$29–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$30. Each module is fed at up to $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$31, with $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$32 peak per segment, and low-latency vehicle-to-infrastructure signaling keeps end-to-end latency below $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$33. The reported transfer efficiency is approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$34–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$35 at $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$36–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$37, dropping below $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$38 outside the $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$39–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$40 range. In the co-simulated $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$41 urban corridor, transferred energy is $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$42–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$43 per $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$44 segment, range-anxiety events fall by $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$45–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$46, deep-discharge cycles fall by approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$47, and battery lifespan increases from approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$48 to approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$49 years. The Delhi case study quotes capital cost of approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$50 million per kilometer, break-even over $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$51–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$52 years on high-utilization corridors, annual energy savings of approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$53, and approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$54 of avoided $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$55 (Agnihotri et al., 14 Dec 2025).

On-road energy can also be coordinated through charging stations, renewables, and vehicle-to-grid participation. "Smart Energy Management with Optimized Prosumerism for Achieving Dynamic Net-Zero Balance in Electrified Road Transport Networks" (Ayaz et al., 2023) models a network comprising the main power grid, distributed wind and PV, EVs as prosumers with bidirectional V2G chargers, charging stations, and 5G-enabled aggregators. Renewable output and EV demand or surplus are forecast hourly using CatBoost, XGBoost, LightGBM, and a CNN-LSTM hybrid for renewables, and CatBoost, XGBoost, LightGBM, and a Transformer for EV velocity and residual SOC. The grid then solves a MILP minimizing

$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$56

subject to capacity, net-zero balance, utility, and surplus-demand bounds. The reported numerical outcomes include an average grid-load reduction of $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$57 relative to no prosumerism, an additional cost saving of $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$58 relative to MILP without EVs, more than $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$59 grid-cost reduction when the grid uses renewables rather than fossil fuels under the $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$60-penalty term, approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$61 surplus utilization at $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$62 of approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$63–$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$64 stations per $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$65 for $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$66 (Ayaz et al., 2023).

A third mechanism is mobile energy storage by moving vehicles themselves. "Compensation of Charging Station Overload via On-road Mobile Energy Storage Scheduling" (Chen et al., 2019) models privately owned PEVs as on-road MES units that charge at resourceful charging stations and discharge at limited-capacity stations. The price interaction between the power system operator and MES owners is formulated as a Stackelberg game with a unique equilibrium. The reported simulations show that when average MES service capacity rises from $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$67 to $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$68, the proposed game-based scheme yields up to $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$69 higher PSO utility than price-minimization and random-pricing benchmarks (Chen et al., 2019). Taken together, these works expand on-road energy from a vehicle-consumption problem into a moving-interface problem linking roads, storage, and power systems.

5. Estimation, calibration, and carbon accounting

Reliable on-road energy management depends on calibration and validation against measured data. The Toyota RAV4 study in (Carpio et al., 27 Mar 2025) is representative of this concern. It begins with a Mid-SUV Autonomie template, modifies engine and driveline parameters, runs a virtual chassis dynamometer over HWFET, US06, and WLTC, and iterates gear-shift logic until internal states and fuel-rate better match the physical chassis-dynamometer data. The improved Autonomie model reduces HWFET fuel-rate MAE from $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$70 to $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$71, while the simplified reduced model achieves $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$72 MAE and only $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$73 cumulative fuel error on the same cycle (Carpio et al., 27 Mar 2025). This validates the reduction pipeline as a semi-principled alternative to fully detailed powertrain simulation.

Open-data estimation of transportation emissions provides a complementary perspective at regional scale. "Estimating On-road Transportation Carbon Emissions from Open Data of Road Network and Origin-destination Flow Data" (Zeng et al., 2024) starts from the standard bottom-up identity

$$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$74

then replaces direct VMT requirements with a hierarchical heterogeneous graph-learning model, HENCE, built from OpenStreetMap road networks and LEHD-LODES OD flows. The model constructs a road-network graph, a community-level heterogeneous graph with spatial and OD links, and a region-level heterogeneous graph, with EGAT message passing and attention-based fusion across edge types and scales. On U.S. county-scale data for 2015 and 2017, HENCE attains $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$75, MAE approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$76, and RMSE approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$77, outperforming the best baselines by approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$78 on $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$79 and approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$80 on MAE (Zeng et al., 2024). The learned attention weights indicate that high-emission regions are more OD-link driven, while low-emission regions are more spatial-link driven (Zeng et al., 2024).

Historical-trip learning also appears in powertrain management. "A Physics Model-Guided Online Bayesian Framework for Energy Management of Extended Range Electric Delivery Vehicles" (Wang et al., 2020) uses in-use telematics from a fleet of series EREVs to update a single rule-based controller parameter, $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$81, after each completed trip. The power demand is computed from longitudinal force balance, the battery SOC evolves through an RC-equivalent model, and the “ideal” $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$82 values across trips are modeled by a Normal-Gamma prior and posterior. Tested on $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$83 real delivery trips from $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$84 vehicles, the method achieves an average fuel-use reduction of $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$85, approximately $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$86 MPGe improvement, and no trip with SOC below $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$87 (Wang et al., 2020). This is a data-assimilation view of on-road energy: the route is not necessarily optimized directly, but the energy-management policy is updated from repeated operational evidence.

6. Conceptual boundaries, recurring misconceptions, and active directions

Several recurring simplifications are contradicted by the cited results. First, energy is not reducible to distance or travel time alone. The Leaf eco-routing system reports up to $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$88 lower energy use than shortest-time routing (Wu et al., 2020), and VPCRO shows that least-cost paths differ from shortest-distance paths for most origin-destination pairs in both conventional and electrified fleets (Qiao et al., 2016). Second, energy is not well represented by symmetric quadratic acceleration penalties. The PCI literature states explicitly that $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$89 penalizes positive and negative accelerations symmetrically and therefore does not distinguish traction from coasting or braking (Hadjigeorgiou et al., 5 Jun 2025). Third, slope and load are not minor corrections. Slope-aware trajectory planning yields $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$90 fuel-efficiency gain for sedans and $$F_{\mathrm{tot}}(v,\theta)=F_{\mathrm{roll}}+F_{\mathrm{aero}}+F_{\mathrm{slope}},\qquad P(v,\theta)=F_{\mathrm{tot}}(v,\theta)\,v,$$91 for diesel trucks over model-agnostic QP planning (Tian et al., 2024), while ALD-EVRP shows that ignoring real-time load underestimates energy consumption (Su et al., 23 Nov 2025).

Another misconception is that negative energy edges make efficient graph search impractical. The online reweighting constructions in (Ahmadi et al., 2024) and the profile-dominance label-setting search in (Ahmadi et al., 1 Dec 2025) show that regenerative braking can be handled without resorting to offline preprocessing or exhaustive profile merging. A related misconception is that high-fidelity models are always necessary. The reduced Toyota RAV4 fuel model in (Carpio et al., 27 Mar 2025) shows that simplified polynomial models can be reliable for large-scale transportation applications, but the same study also makes clear that their fidelity tracks the quality of the calibrated reference model. This suggests that model reduction and model calibration are not competing goals; they are sequential requirements.

The surveyed papers also identify open directions rather than a single settled architecture. Several works propose transfer to mixed fleets, hybrids, and EVs by changing fitted fuel-rate or power models (Tian et al., 2024, Moehle, 2023). Others point to deeper integration with infrastructure forecasts, HD maps, V2X, and smart-grid coordination (Ayaz et al., 2023, Agnihotri et al., 14 Dec 2025). Future extensions named explicitly in the corpus include multi-vehicle platoons and full vehicle tests for EMATO (Tian et al., 2024), speed-dependent emission factors and vehicle-type shares for HENCE-style carbon accounting (Zeng et al., 2024), real-time adaptation of rule-based EREV parameters during a trip (Wang et al., 2020), and experimental validation under sensor noise, road-grade variations, and multi-vehicle deployment for ECO+ (Hadjigeorgiou et al., 5 Jun 2025). Finally, the lateral-dynamics study (Kumari et al., 20 May 2025) indicates that cornering losses remain underrepresented in many state-of-the-art estimators. This suggests that the present definition of on-road energy is still expanding: from longitudinal motion and route choice toward a fuller accounting of maneuvering, infrastructure coupling, and energy exchange while in motion.