102 both compared to vehicles traveling alone and compared to platooning vehicles with typical fixed following distances.

Referring now to FIG. 2, components of an illustrative vehicle 102 are shown. The vehicle 102 may be embodied as a semi-truck, a tractor, a class 8 truck, or other vehicle. As shown in FIG. 1, the vehicle 102 includes a computing device 120, a GPS system 122, a radar system 124, and a communication subsystem 126. The computing device 120 may be embodied as a computer, an embedded computer, an industrial computer a mobile device, a microprocessor, a microcontroller, and/or other control circuitry. For example, the computing device 120 may be embodied as a ruggedized industrial computer for vehicular or embedded use. Accordingly, the computing device 120 may include a processor, an I/O subsystem, memory, a data storage device, and/or other components commonly found in an industrial computer. In operation, the computing device 120 may store various data and software used during operation of the vehicle 102 such as operating systems, applications, programs, libraries, and drivers.

The GPS system 122 may be embodied as a global positioning system (GPS) receiver, a Galileo receiver, a GLONASS receiver, a global navigation satellite system (GNSS) receiver, or other location circuitry capable of determining the precise coordinates of the vehicle 102. The radar system 124 may be embodied as a forward-facing radar capable of determining the distance between the vehicle 102 and a preceding vehicle (e.g., a leader 104 or preceding follower vehicle 106). In other embodiments, the vehicle 102 may include a lidar system or similar rangefinding device. The communication subsystem 126 may be embodied as a short-range wireless communication system enabling vehicle-to-vehicle communications between the vehicle 102 and other vehicles 102 in the system 100. For example, the communication subsystem 126 may include one or more dedicated short range communication (DSRC) radios operating at 5.9 GHz. The GPS system 122, the radar system 124, and the communications subsystem 126 are coupled to the computing device 120, which processes data generated by those devices. For example, the computing device 120 may communicate data via Ethernet with a DSRC radio, which may exchange the data wirelessly with DSRC radios of other vehicles 102.

The computing device 120 is also coupled to a controller area network (CAN) bus 128, which is a vehicle bus for communication between components of the vehicle 102, and is illustratively a J1939 bus for communication among components of a heavy vehicle. In some embodiments, the computing device 120 may communicate with devices connected to the CAN bus 128 via a CAN gateway or other communication devices. As shown, the CAN bus 128 may be coupled to multiple components including an emergency stop control 130, low-level by wire system 132, and one or more electronic control unit(s) (ECU(s)) 134. The low-level by wire system 132 may allow for computerized control of one or more components of the vehicle 102, including engine torque (e.g., acceleration), braking, and in some embodiments, steering. The emergency stop control 130 may allow a driver or other user to terminate automatic control of the vehicle 102 if unsafe conditions occur. The ECUs 134 may include engine controllers, throttle controllers, transmission controllers, braking controllers, steering controllers, and/or other control devices of the vehicle 102.

As discussed in more detail below, the vehicles 102 may be configured to transmit and receive data with each other and/or other devices of the system 100 over one or more direct wireless links or, in some embodiments, a network. The network may be embodied as any number of various wired and/or wireless networks. For example, the network may be embodied as, or otherwise include, a cellular network (e.g., a 3G LTE, 4G, or 5G network), a wired or wireless wide area network (WAN), a wired or wireless local area network (LAN), and/or a publicly-accessible, global network such as the Internet. As such, the network may include any number of additional devices, such as additional computers, routers, and switches, to facilitate communications among the vehicles 102 of the system 100.

Referring now to FIG. 3, in the illustrative embodiment, a vehicle 102 establishes an environment 300 during operation. The illustrative environment 300 includes a lookahead cruise controller 302 and a lookahead headway controller 306. The various components of the environment 300 may be embodied as hardware, firmware, software, or a combination thereof. As such, in some embodiments, one or more of the components of the environment 300 may be embodied as circuitry or a collection of electrical devices (e.g., lookahead cruise controller circuitry 302 and/or lookahead headway controller circuitry 306). It should be appreciated that, in such embodiments, one or more of those components may form a portion of the computing device 120 and/or other components of the vehicle 102.

The lookahead cruise controller 302 is configured to control velocity of the leader vehicle 104 within a predetermined route 110 based on a grade profile of the predetermined route 110. The grade profile may be embodied as grade profile data 310 stored by or otherwise accessible by the computing device 102. The lookahead cruise controller 302 may be further configured to communicate vehicle state data for the leader vehicle 104 to a follower vehicle 106. Controlling velocity of the leader vehicle 104 may include determining a torque trajectory and a velocity trajectory using nonlinear model predictive control with a cost function based on predicted velocity error and predicted fuel consumption. Determining the torque trajectory and the velocity trajectory may further include simulating vehicle position and vehicle velocity using a nonlinear longitudinal vehicle model with the grade profile 310, evaluating the cost function based on simulating the vehicle position and the vehicle velocity, and determining the torque trajectory by minimizing the cost function. Simulating the vehicle position and the vehicle velocity may further include calculating a derivative of the vehicle position comprising the vehicle velocity, and calculating a derivative of the vehicle velocity comprising a vehicle acceleration. In some embodiments, one or more of those functions may be performed by one or more sub-components, such as a nonlinear model predictive controller 304.

The lookahead headway controller 306 is configured to control velocity of the follower vehicle 106 within the predetermined route 110 based on a headway distance 108 between the follower vehicle 106 and the leader vehicle 104 and the grade profile 310 of the predetermined route 110. Controlling the velocity of the following vehicle 106 may include determining a torque trajectory and a velocity trajectory using a nonlinear model predictive control with a cost function based on predicted headway error, predicted headway rate of change, and predicted fuel consumption. Evaluating the cost function may include determining wheel speed of the follower vehicle 106 with a nonlinear longitudinal vehicle model; determining engine speed based on the wheel speed, determining engine torque based on the engine speed and a torque curve associated with the follower vehicle 106, and determining the predicted fuel consumption based on the engine torque and the engine speed. Determining the torque trajectory and the velocity trajectory may further include simulating headway, leader velocity, and follower velocity with a nonlinear longitudinal vehicle model with the grade profile 310 of the predetermined route, evaluating the cost function based on the simulated headway, leader velocity, and follower velocity, and determining the torque trajectory by minimizing the cost function. Simulating the headway, the leader velocity, and the follower velocity may further include calculating a derivative of the headway comprising a change in headway, calculating a derivative of the leader velocity comprising a damped leader acceleration, and calculating a derivative of the follower velocity comprising a follower acceleration. Simulating the headway, the leader velocity, and the follower velocity may further include receiving leader velocity data and/or leader acceleration data from the leader vehicle via a vehicle-to-vehicle communication link. Calculating the derivative of the headway may include calculating a difference between the leader velocity data and follower velocity data. Calculating the derivative of the leader velocity may include applying a first order decay to the acceleration data. In some embodiments, controlling the velocity of the follower 106 vehicle may include determining a torque trajectory and a velocity trajectory using a string-stable controller. In some embodiments, one or more of those functions may be performed by one or more sub-components, such as a nonlinear model predictive controller 308.

Referring now to FIG. 4, in use, each vehicle 102 of the system 100 may execute a method 400 for optimal vehicle platooning control. It should be appreciated that, in some embodiments, the operations of the method 400 may be performed by one or more components of the environment 300 of the vehicle 102 as shown in FIG. 3. The method 400 begins with block 402, in which the vehicle 102 determines a grade profile for a predetermined route 110. The grade profile includes data indicative of the grade 114 (e.g., angle or other measure of steepness) of the route 110 at each position 112 along the route 110. The grade profile may be determined, for example, using predetermined mapping data, recorded grade information, or other predetermined data. The grade profile may be determined by the vehicle 102 and/or provided to the vehicle 102 by another device such as another vehicle 102 or another connected or remote computing device.

In block 404, the vehicle 102 determines any parameters required for one or more vehicle models associated with the vehicle 102. For example, the vehicle 102 may determine mass, gear ratios, engine power, engine torque curves, fuel consumption models, or other vehicle-specific data. In some embodiments, the vehicle parameters may be predetermined and stored ahead of time for the vehicle 102. In some embodiments, the vehicle parameters may be updated based on sensor data or otherwise updated before each trip. For example, effective mass of the vehicle 102 including mass of any trailers or other cargo may be determined for each trip.

After determining parameters of the route 110 and each vehicle 102, the method 400 as executed by the leader vehicle 104 proceeds to block 406, and the method 400 as executed by each follower vehicle 106 proceeds to block 410. The method 400 continues in parallel, with each vehicle 102 controlling its velocity over the route 110 as described further below.

In block 406, the leader vehicle 104 is controlled for optimized fuel consumption based on the grade profile. The computing device 120 of the lead vehicle 104 may, for example, control an input such as torque and/or velocity while using the grade profile to optimize fuel consumption. For example, with knowledge of an upcoming steep ascent, the computing device 120 may increase speed, which may allow the vehicle 102 to ascend the hill without dropping below a minimum speed and without requiring gear shifting. As another example, with knowledge of an upcoming steep descent, the computing device 120 may decrease speed, which may allow the vehicle 102 to descend without exceeding a maximum speed and without requiring braking. The computing device 120 may use any appropriate control techniques to optimize fuel consumption. In at least one embodiment, the computing device 120 uses nonlinear model predictive control (NMPC) to optimize fuel consumption. One potential embodiment of a method for NMPC control for the leader vehicle 104 is shown in FIGS. 5 and 6 and described further below. Additionally or alternatively, in other embodiments the computing device 120 may use other control techniques, such as linear model predictive control, predictive cruise control, or other control system.

In block 408, the leader vehicle 104 may communicate vehicle state with other vehicles 102 of the system 100. The leader vehicle 104 may, for example, communicate data indicative of velocity, acceleration, or other vehicle state data with one or more follower vehicles 106. After communicating vehicle state data, the method 400 loops back to block 406 to continue controlling the leader vehicle 104.

Referring again to block 404, the method 400 as executed by each follower vehicle 406 proceeds to block 410, in which the follower vehicle 106 is controlled for optimized fuel consumption with variable headway 108 based on the grade profile. The computing device 120 of the follower vehicle 106 may, for example, control an input such as torque and/or velocity while using the grade profile to optimize fuel consumption. For example, based on knowledge of upcoming terrain, the computing device 120 may increase or decrease the headway 108 between the follower vehicle 106 and the preceding vehicle 102 (e.g., the leader vehicle 104 or another follower vehicle 106) in order to optimize fuel consumption. The computing device 120 may use any appropriate control techniques to optimize fuel consumption. In at least one embodiment, the computing device 120 uses nonlinear model predictive control (NMPC) to optimize fuel consumption. One potential embodiment of a method for NMPC control for the follower vehicle 106 is shown in FIGS. 5 and 7 and described further below. Additionally or alternatively, in other embodiments the computing device 120 may use other control techniques, such as linear model predictive control, string-stable control such as H-infinity optimal control, or other control system.

In block 412, the follower vehicle 106 may communicate vehicle state with other vehicles 102 of the system 100. The follower vehicle 106 may, for example, communicate data indicative of velocity, acceleration, or other vehicle state data with the leader vehicle 104 and/or with one or more other follower vehicles 106. After communicating vehicle state data, the method 400 loops back to block 410 to continue controlling the follower vehicle 104.

Referring now to FIG. 5, in use, each vehicle 102 of the system 100 may execute a method 500 for nonlinear model predictive control. It should be appreciated that, in some embodiments, the operations of the method 500 may be performed by one or more components of the environment 300 of the vehicle 102 as shown in FIG. 3. The method 500 begins with block 502, in which the computing device 120 of the vehicle 102 determines one or more parameters for a nonlinear model of the vehicle 102. The parameters may be determined empirically or analytically, and in some embodiments may be predetermined and stored or otherwise programmed into the computing device 120.

In block 504, the computing device 120 determines a longitudinal vehicle model for the vehicle 102. The longitudinal vehicle model may be embodied as one or more differential equations that describe and predict longitudinal motion of the vehicle 102, including dynamic acceleration and deceleration behavior. In some embodiments, the longitudinal vehicle model may be embodied as Equation 1, below. In Equation 1, X is vehicle longitudinal position, {dot over (X)} is vehicle speed, and {umlaut over (X)} is vehicle acceleration. M_effis effective mass of the vehicle and trailer, and may be calculated according to Equation 2, below. B_effis an effective damping coefficient that may be calculated according to Equation 3, below, and D is a drag coefficient. τ_engis engine torque, η_diffis differential gear ratio (e.g., final drive), and η_transis transmission gear ratio. F_rris force due to rolling resistance, and F_gradeis force due to grade. Accordingly, F_grademay be determined for any position X along the route 110 based on the grade profile determined as described above.

M
eff

⁢

X
¨

+

B
eff

⁢

X
.

+

D
⁢

X
.

2

=

τ
eng

*

η
diff

*

η
trans

r
eff

-

F
rr

-

F
grade

(
1
)

M
eff

=

(

M
tractor

+

M
trailer

)

+

J
diff

R
w
2

+

J
eng

⁢

η
diff
2

⁢

η
trans
2

R
w
2

(
2
)

B
eff

=

B
diff

+

B
trans

*

η
diff
2

+

B
eng

*

η
diff
2

*

η
trans
2

R
w
2

(
3
)

In some embodiments, in block 506 the computing device 102 may determine a headway model. For example, each follower device 106 may determine a headway model. The headway model may be embodied as one or more differential equations that describe and predict the headway 108 between the vehicle 102 and the preceding vehicle in the system 100, such as the leader vehicle 104 or another follower vehicle 106. Similar to the longitudinal vehicle model, the headway model is also determined based on the grade profile for the route 110. In particular, in some embodiments the headway model may include calculating vehicle velocity and/or acceleration using the Equations 1-3 as described above.

After determining parameters for one or more models, the method 500 proceeds block 508, in which the computing device 120 determines velocity and torque trajectories using nonlinear model predictive control (NMPC) and an objective function. The velocity and torque trajectories define input to the system (e.g., the vehicle 102) over a control horizon (in time or distance), and may be embodied as a series of torque values and optimal velocity values. The torque values may be used, for example, to control the vehicle 102 using the low level by wire system 132. The vehicle 102 may, for example, activate the throttle and/or service brakes according to values of the torque trajectory. As part of NMPC, the computing device 120 simulates behavior of the vehicle 120 into the future using the nonlinear model of the vehicle described above. The computing device 120 uses an optimizer (e.g., a nonlinear programming (NLP) optimizer) to find the optimal velocity and torque trajectories based on the objective function. As described further below in connection with FIGS. 6 and 7, the objective function includes fuel consumption as a weighted term. The particular objective function used may vary between the leader vehicle 104 and the follower vehicles 106. For example, as shown in FIG. 6 and described further below, the objective function for the leader vehicle 104 may be based on fuel consumption and speed error. As another example, as shown in FIG. 7 and described further below, the objective function for each follower vehicle 106 may be based on fuel consumption, headway error, and headway rate of change error.

In the illustrative embodiment, the computing device 120 may execute a nested control structure in order to improve performance. In block 510, in an outer loop, the computing device 120 generates a feedforward torque profile and optimal velocity profile with the NLP optimizer. As described above, the computing device 120 may simulate behavior of the vehicle 102 and optimize for fuel consumption. In block 512, in an inner loop, the computing device 120 generates torque compensation based on a measured velocity error from the optimal velocity profile. The torque compensation may be embodied as a corrective torque value generated by a PID controller or other controller based on the velocity error. In block 514, the computing device 120 controls the vehicle 102 based on the feedforward torque combined with the torque compensation. The computing device 120 may, for example, dispatch one or more torque commands to the low-level by wire system 132 via the CAN bus 128. In block 516, the computing device 120 may communicate one or more vehicle states with other vehicles 102. As described above, the computing device 120 may send and/or receive vehicle state data including vehicle speed and acceleration with the other devices 102. In block 518, the computing device 120 monitors velocity in the inner loop. The computing device 120 may calculate velocity error compared to the optimal velocity profile and then feed that velocity error back to the inner loop controller as described in block 512. In block 520, the computing device 120 monitors torque, grade, braking, and velocity in the outer loop. The computing device 120 may calculate error and/or otherwise feed that data back to the NMPC controller as described in block 510. Using the nested feedback loop arrangement shown in FIG. 5, the computing device 120 may reliably achieve output rates necessary for real time control. For example, in an embodiment the computing device 120 may achieve a 20 Hz control rate. Of course, in other embodiments a different control arrangement may be used. For example, some embodiments may including a single NMPC control loop.

Referring now to FIG. 6, in use, a leader vehicle 104 of the system 100 may execute a method 600 for nonlinear programming optimization. It should be appreciated that, in some embodiments, the operations of the method 600 may be performed by one or more components of the environment 300 of the vehicle 102 as shown in FIG. 3. Additionally or alternatively, in some embodiments the method 600 may be executed in an outer control loop as described above in connection with block 510 of FIG. 5. The method 600 begins with block 602, in which the computing device 120 of the leader vehicle 104 propagates vehicle states in the grade profile using simulation with the nonlinear longitudinal vehicle model described above. Illustratively, two vehicle states x₁, x₂are defined as vehicle position and vehicle velocity, respectively. In block 604, the computing device 120 simulates values for vehicle position and vehicle velocity using derivatives of those states. In particular, the derivative {dot over (x)}₁is the velocity x₂, also denoted v_x. The derivative

x
.

2

=

x
¨

1

=

a
x

,

which is the acceleration of the vehicle. This acceleration a_xmay be calculated using the longitudinal vehicle model described above in connection with Equations 1 through 3. The computing device 120 may propagate states forward using the Runge-Kutta 4th order method or any other appropriate technique.

In block 606, the computing device 120 of the leader vehicle 104 evaluates a cost function associated with the propagated vehicle states. The leader vehicle 104 cost function is based on velocity error compared to a target velocity (e.g., 55 miles per hour, 25 meters per second, or other setpoint) and fuel consumed. An illustrative cost function J_eco-cruiseis shown in Equation 4, below. In the illustrative cost function, Q₁and Q₂are tunable weights to yield desired performance. If Q₂is zero, then the computing device 120 will aggressively track the desired set speed. When Q₂is increased, the computing device 120 allows the speed of the vehicle 102 to fluctuate over hills, which may save fuel. As an example, the computing device 120 may allow the vehicle 102 to coast over the desired set speed while going down a hill so that the vehicle 102 carries more kinetic energy into the next hill, which may require less fuel to power back to speed.

J

e
⁢
c
⁢
o

-
cruise

=

Q
1

⁢

∑

Err

v
⁢
e
⁢
l

2

+

Q
2

⁢

∑

fuel

c
⁢
o
⁢
n
⁢
s
⁢
u
⁢
m
⁢
e
⁢
d

2

(
4
)

The cost function shown in Equation 10 is in terms of fuel consumed. The value of fuel consumed may be determined based on the longitudinal model described above in connection with Equations 1-3. In particular, Equation 1 may be used to determine vehicle speed, which is related to wheel speed. Wheel speed ω_wheelmay be converted to engine speed ω_engbased on differential and transmission gear ratios as well as wheel radius, as shown in Equation 5, below. Engine speed may be converted to engine torque using a torque curve associated with the engine of the vehicle 102. Each engine may have a particular torque curve, which may be supplied by the engine manufacturer, measured, or otherwise determined. In the illustrative embodiment, the torque curve of the engine is modeled as a third-order polynomial that is fit to a published torque curve for the engine of the vehicle 102, as shown in Equation 6. Next, engine torque is converted to fuel consumption. Illustratively, engine torque may be converted to fuel consumption using brake-specific-fuel-consumption (BSFC), which is a functional relationship from engine power and engine speed to fuel rate. Each engine may have an associated BSFC map, which may be provided by an engine manufacturer or may be determined experimentally. For example, data may be collected for engine power, engine speed, and fuel rate and a model may be created using least-squares fitting. The computing device 120 may use a linear model as shown in Equation 7 or a non-linear model as shown in Equation 8.

ω
eng

=

π
30

⁢

η
diff

*

η
trans

R
w

*

ω
wheel

(
5
)

τ
eng

=

c
1

⁢

ω
3

+

c
2

⁢

ω
2

+

c
3

⁢
ω

+

c
4

(
6
)

m
.

fuel

=

Pow
eng

*

b
0

(
7
)

m
.

fuel

=

Pow
eng
2

*

ω
eng

*

b
0

+

Pow
eng

*

ω
eng

*

b
1

+

Pow
eng

*

b
2

(
8
)

In block 608, the computing device 120 solves for optimal torque (including engine torque and/or service brake application) over the control horizon by minimizing the cost function. To minimize the cost function, the computing device 120 may use any appropriate nonlinear programming optimizer or other optimization technique. For example, in the illustrative embodiment the computing device 120 performs a direct multiple shooting operation to solve for an optimal control horizon. After optimizing a torque trajectory over the control horizon, the computing device 120 may continue to control the vehicle 102 and, accordingly, repeatedly execute the method 600. For example, the computing device 120 may use the torque trajectory to perform inner-loop control operations as described above in connection with FIG. 5, and the computing device 120 may execute the method 600 repeatedly during each execution of the outer control loop as described above.

Referring now to FIG. 7, in use, a follower vehicle 106 of the system 100 may execute a method 700 for nonlinear programming optimization. It should be appreciated that, in some embodiments, the operations of the method 700 may be performed by one or more components of the environment 300 of the vehicle 102 as shown in FIG. 3. Additionally or alternatively, in some embodiments the method 700 may be executed in an outer control loop as described above in connection with block 510 of FIG. 5. The method 700 begins with block 702, in which the computing device 120 of the follower vehicle 106 propagates vehicle states in the grade profile using simulation with the nonlinear headway model described above. Illustratively, the headway model may define three states x₁, x₂, x₃, as shown in Equations 9 through 11, below. In particular, state x₁is the headway 108, state x₂is the speed of the preceding vehicle 102 (labeled vehicle i+1 and, e.g., the leader vehicle 104 or preceding follower vehicle 106), and state x₃is the velocity v_x(i)of the current vehicle 102. In block 704, the computing device 120 simulates values for headway, preceding vehicle velocity, and current vehicle velocity using derivatives of those states, which are shown in Equations 12 through 14 below. The derivative {dot over (x)}₁is the change in headway and is equal to the difference between the preceding vehicle speed x₂and the current vehicle speed x₃. Derivative {dot over (x)}₂is the damped acceleration of the preceding vehicle 102. As shown, a first order decay is applied to the preceding vehicle acceleration, and the velocity profile of the preceding vehicle is generated using a decaying acceleration model. This may improve string stability for following vehicles 106. State data for other vehicles (e.g., the preceding vehicle) may be shared using vehicle to vehicle communication or otherwise communicated between vehicles. Derivative {dot over (x)}₃is the acceleration of the current vehicle 102, which may be determined using the longitudinal vehicle model described above in connection with block