TRAJECTORY CALCULATION SYSTEM MINIMIZING ENERGY CONSUMPTION OF AN INTERNAL COMBUSTION ENGINE

Abstract

The invention relates to a computer-implemented calculation system for determining a trajectory while minimizing the energy consumption of an internal combustion engine vehicle. The system comprises: - a dynamics model module (M1) and an energy consumption model module (M2) configured to define driving parameters; - an optimization module (M3) configured to define driving constraints based on the driving parameters; - a trajectory determination module (M4) using calculations based on a Pontryagin minimum principle that minimizes a Hamiltonian function of said driving parameters. In particular, the computer-implemented calculation steps are performed by the vehicle's onboard computer. Figure 1

Description

Title of the invention: TRAJECTORY CALCULATION SYSTEM MINIMIZING ENERGY CONSUMPTION OF A MOTOR VEHICLE WITH AN INTERNAL COMBUSTION ENGINE

[0001] The invention relates to a calculation system for determining a vehicle speed trajectory while minimizing the vehicle's energy consumption for the same travel time. The system is suitable for internal combustion engine vehicles. The invention further relates to a calculation method and a corresponding computer program.

[0002] Numerous tips and training courses on economical driving (generally called "eco-driving") are shared to limit vehicle energy consumption. However, these tips do not guarantee an actual reduction in consumption for a given route, considering a given travel time and initial speed trajectory.

[0003] A calculation method for guaranteeing an eco-driving trajectory, that is, a speed trajectory minimizing energy consumption for the same travel time as the initial speed trajectory, has been developed previously. It consists of using a dynamic programming algorithm to calculate the optimal speed trajectory by considering: - a cost function (energy expenditure): the vehicle's consumption; - the dynamics of the system: the speed of the vehicle; - the multiple constraints of the problem: travel time, regulated speeds and maximum accelerations of the vehicle.

[0004] To calculate this optimal speed trajectory, dynamic programming relies on calculating each optimal speed sub-trajectory. Indeed, recursively, for a given distance segment and at each initial speed, all possible speed variations are evaluated (according to the cost function), and the best variation is retained for each initial speed. The next distance segment then uses the previous results to construct the sequence of optimal trajectories.

[0005] Unfortunately, this methodology can only have a good level of optimality if there is a good discretization of the vehicle speed steps and distance traveled.

[0006] Furthermore, this method has the drawback of significant computation time (several minutes), high computing power, and high memory size since all eventualities are calculated. Consequently, an embedded application and Real-time implementation of this algorithm is not feasible.

[0007] A known solution to this problem is detailed in patent document FR 3 124 147 A1. This document describes a computer-implemented calculation system for determining a trajectory while minimizing the energy consumption of a motor vehicle. The system comprises a dynamics and energy consumption modeling module configured to define driving parameters, an optimization module configured to define driving constraints based on these driving parameters, and a trajectory determination module. More specifically, this last module calculates an energy-efficient speed trajectory using a set of analytical equations that solve a simplified version of the eco-driving problem for electric or hybrid vehicles.These analytical solutions (in the form of speed profiles to be applied) are deduced using Pontryagin's minimum principle, which minimizes a Hamiltonian function of the driving parameters. The solution described in this document relies on a specific expression of the eco-driving problem compatible with a fast and low-error solution using Pontryagin's minimum principle. Ultimately, this solution allows the calculation of an eco-driving trajectory to be integrated into a vehicle or a mobile application. The solution can thus be implemented in real time and allows this type of algorithm to be embedded in an automotive computer or a mobile phone. To achieve this, two problems are solved simultaneously: - significantly reduce the computing power, processing time, and memory required to obtain an eco-driving trajectory; and - maintain an optimality close to the calculation by dynamic programming while respecting the end of travel time constraint while proposing a reduction in consumption compared to the original (non-optimized) cycle.

[0008] However, a drawback of the solution described in this patent document is that it is not applicable to internal combustion engine vehicles (conventional vehicles), which nevertheless constitute the majority of the vehicles currently on the road. Furthermore, the solution described in patent document FR 3 124 147 A1 does not take into account the vehicle's acceleration limits, nor the adaptation of the final conditions of the calculated subtrajectories when the various constraints are incompatible.

[0009] To overcome the shortcomings of the prior art, the invention proposes a computer-implemented calculation system for determining a trajectory while minimizing the energy consumption of a motor vehicle with an internal combustion engine, the system comprising: - a configured dynamics and energy consumption modeling module to define driving parameters, - an optimization module configured to define driving constraints based on driving parameters, - a trajectory determination module by calculations according to a Pontryagin minimum principle minimizing a so-called Hamiltonian function of said rolling parameters; The dynamic model is defined according to the equations: s(t)=v(t) (1) v(t)=p(t)T( / )−ub(t)−Cq+_(2c2vz+q)(6) Or s is the position of the vehicle (in m); v is the speed of the vehicle (in m / s); f is the time (in s); is a variable associated with the vehicle's speed ratio; P — mr^ is a coefficient indicating the efficiency of the vehicle's transmission; ^gb is a coefficient indicating the efficiency of the vehicle's gearbox; Rt is the transmission speed ratio; RGB is the selected current speed ratio; m is the mass of the vehicle in kg; 1 tire is the radius of the wheel (in m). T is the engine torque control of the vehicle (in Nm); is the braking command (in m / s2); C0 = «0 / m; — at + mg sin(0(s)) is the rolling and slope resistance (in N); â is the rolling resistance at zero speed (in N); 0 is the slope of the road (in rad); 6i is the rolling resistance of the vehicle (in N / (m / s) / kg); c2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2) / kg); vt is a velocity value (in m / s) chosen so that the dynamics model and the energy consumption model are linearized at the level of this velocity value; The energy consumption model is defined by the equation: pM= z^+WJ fa+2i.0)^r)2+sy <dt U t ) + VJ t k ( t ) d t + Zouyr / d ' ' r2 \ \ ' \ ! ' \ I OR Pr is the power drawn from the vehicle's fuel tank (in W); is the lower heating value of the fuel (in Ws / g); Y rp is a coefficient expressed in g / s; is a coefficient expressed in gs / rad2; ?r,2 is a coefficient expressed in g / rad; ^r.3 is a coefficient expressed in g / (rad.Nm); 1¼ is a coefficient expressed in g / (Nm.s)

[0010] In the context of the invention, the term "module" is understood as a set of hardware elements and program code instructions to perform a given action, in particular a calculation.

[0011] The calculation system according to the invention is adapted for a motor vehicle with an internal combustion engine and makes it possible to obtain, accurately and with low computing power, an optimal speed trajectory for such a vehicle while minimizing its energy consumption for the same travel time. The proposed invention also constitutes an analytical solution to the eco-driving problem using Pontryagin's Minimum principle. This solution relies on a specific expression of the eco-driving problem compatible with a fast and low-error solution using Pontryagin's Minimum principle. Ultimately, this solution makes it possible to integrate the calculation of an eco-driving trajectory into an automotive computer or into a mobile phone application, for example.The proposed invention also makes it possible to determine vehicle dynamics based on parameters accessible to a computer in a corresponding vehicle, to obtain theoretical route optimization, and to determine the route with simplified calculations that limit processor processing time. The proposed invention also makes it possible to obtain acceleration profiles suitable for both eco-driving and more "aggressive" driving. Finally, by taking into account the vehicle's coasting phases (particularly due to the fact that both the vehicle's engine torque control T and the braking control ub can be impaired at certain times), the calculation system is more precise than prior art calculation systems (and therefore more efficient in terms of minimizing the vehicle's energy consumption).

[0012] According to one variant, the optimization module is configured to solve the following equations: / / (10) min L (L(T, v) +^) dt {r(t),p(t),u(t)j(t),v(t),t0 according to s( / )=v(0 (11) v(j) = p(t)T(j)-u^+ (12) ^)=¾ <13> ■'(7)=sf <14) v( / 0)=v0 (15) v(tf)-Vf (16) ^min — ^ ( 0 — -amin <a(t) <amax (18) Q <ub(t) <ub,nax (19) Q <T(t) <Tmax (20) P ( 0 { P [y P f • ' ' ' PNsh | Or L is the instantaneous energy consumption of the vehicle (in W); P is the penalty that prioritizes travel time over energy gain; *0, sf are the initial and final position constraints; ' o, vf are the initial and final velocity constraints; lmm, vmax are the minimum and maximum speed constraints; amin^ Umax are the minimum and maximum acceleration constraints; ubmax is the maximum braking stress; Tmax is the maximum engine torque constraint; Pq-, P^ ■ • •, Av^sont coefficients relating to a set of vehicle speeds vgp{p) indicate when to change from one speed ratio to another

[0013] This allows for a theoretical optimization of the route, adapted for a motor vehicle with a thermal engine.

[0014] According to one variant, the determination modulus is configured to minimize the so-called Hamiltonian function: H— P(ll v) + P + Xs v + ÀyV (22) Or and A are variations of co-states, each weighting each dynamic. the co-state variations weighting each dynamic, being calculated as follows: 2,= .ÜU=0 (23) A as And (24) V 47 V The optimal, unconstrained braking control is preferably then deduced: 4^=0 (25) dub And " = 0 (26) al and the optimal braking control constraint is also preferably deduced according to: * _ 0, if A,, < 0 (27) ~ . ci JS n ^b.inav A v \J and the optimal motor torque control constraint is also preferably deduced according to: [ Tnutx, if y^ > 0 (28) 7(0* = «^ = 0 [ 0, if { < 0 Or v t ( = w / O+w / ^M) ; with = 0; and _ c0+c2i / -( 2¾^^)^ ; Being a singular couple command defining an a~ M constant speed phase such that _ C^rC^ v^“2q+ ~ Zz^jKt ) ' 2 2¾^ Ultimately, the system of equations described is defined as follows: X = H(t) x(t) X = {5, V, 1, 4, AJ (29) (30)

[0015] This allows for a determination of the path with simplified calculations limiting the processor calculation time.

[0016] According to one variant, the calculation system further includes a module for calculating average speed over a horizon, taking into account information on speed limits, obstacles, and traffic as a function of distance, preferably with a margin on this speed. This allows for precise calculations of the journey parameters, in particular the journey time.

[0017] According to one variant, the calculation system further includes a penalty calculation module having an impact on the average speed according to the equation WtDc = j (tz + a^v + a2v2) + f (29) with V-Vref+ € Or, ^ref is the average speed of the original driving cycle (in m / s) e is a parameter to be calibrated in order to achieve the desired travel time (in m / s) ai is the rolling resistance of the vehicle (in N / (m / s) a2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2)

[0018] This helps to limit errors in calculating journey parameters, in particular journey time.

[0019] According to one variant, the calculation system further includes a module for calculating optimal cruising speed according to the equation vopi,c = arg min (31) Or, w, T is the engine speed and torque associated with the speed V (in rad / s and N / m); V is the speed window used for the search for v'>ptp (in m / s); T) is the engine fuel consumption map; z is the scaling factor associating the time penalty with the optimal constant speed and zihv.

[0020] This makes it possible to compensate for the absence of the aerodynamic resistance term in the acceleration dynamics of the vehicle, which could lead to an optimal speed that would underestimate the energy gain of a lower speed.

[0021] The invention further relates to a computer-implemented method comprising steps for carrying out the actions and / or calculations of the calculation system according to the invention.

[0022] The method can be implemented in a motor vehicle computer.

[0023] Another object of the invention relates to a computer program product comprising program code instructions for executing the steps of a computer-implemented method according to the invention, or steps for carrying out the actions and / or calculations of the computing system according to the invention, when said program is running on a computer.

[0024] The program product can be loaded into the memory of a motor vehicle computer, serving as a computer.

[0025] The invention also relates to a motor vehicle comprising a thermal engine and a computing system according to the invention or a computer program product according to the invention.

[0026] The invention will be further detailed by the description of non-limiting embodiments, and on the basis of the attached [Fig.1] illustrating a method of implementing a system according to the invention.

[0027] The invention relates to an analytical solution to the eco-driving problem using Pontryagin's Minimum principle. This solution relies on a specific expression of the eco-driving problem compatible with a fast and low-error solution using Pontryagin's Minimum principle. Ultimately, this solution allows for the calculation of an eco-driving trajectory to be integrated into a vehicle or mobile application.

[0028] More specifically, the invention proposes a computer-implemented calculation system to determine a trajectory while minimizing the energy consumption of a motor vehicle with an internal combustion engine.

[0029] The system comprises: - a dynamics model module M1 and energy consumption module M2 configured to define driving parameters, in particular in a step S1 of defining driving parameters such as maximum and minimum accelerations, and maximum speed, and other parameters of this type; - an M3 optimization module configured to define driving constraints such as speed limits, obstacles, lights, stopping areas (or stops) according to the distance to be travelled, based on said driving parameters.

[0030] Furthermore, the calculation system is characterized by - a trajectory determination module M4 by calculations according to a Pontryagin minimum principle minimizing a so-called Hamiltonian function of said driving parameters, with in particular a target of travel times over a horizon.

[0031] The invention is adapted for a motor vehicle with an internal combustion engine and makes it possible to obtain, accurately and with low computing power, an optimal speed trajectory for such a vehicle while minimizing its energy consumption for the same travel time. Furthermore, the invention significantly reduces the computing power, processing time, and memory required to obtain an eco-driving trajectory; and maintains an optimality close to that achieved through dynamic programming by respecting the travel time constraint while offering a reduction in consumption compared to the original (non-optimized) cycle. The invention thus makes it possible to integrate this type of algorithm into an automotive computer or a mobile phone. The proposed invention also makes it possible to obtain smoothed acceleration and trajectory profiles suitable for eco-driving.

[0032] In order to obtain a calculation method that is compatible in terms of optimality and computation time, the analytical solution consists, according to the preferred variant, of mathematically describing the problem so that it is compatible with a fast solution using Pontryagin's minimum principle: - The models of vehicle dynamics and energy consumption are simplified while limiting the loss of accuracy compared to the models used in dynamic programming. The optimization method is Pontryagin's minimum principle. This principle minimizes a function, the Hamiltonian, which contains the cost (here, the vehicle's instantaneous fuel consumption), the weighted dynamics of speed and acceleration, and a penalty on travel time. Optimizing a segment is then faster since it consists of solving a problem at both ends (Two Points Boundary Value Problem). - In the preferred variant, each Hamiltonian is expressed in such a way as to solve a piecewise optimization problem while taking into account the final states of the previous piece as well as the initial states of the next piece. The assembly of these Hamiltonians then yields a linear system with variable time and constant piecewise dynamics.

[0033] The technical advantages of this invention, according to the preferred variant, are: - a significant reduction in calculation time compared to dynamic programming: divided by 250 on average; - The previous point leads to a significant decrease in computing power and memory size required to perform the calculation. Thus, it is conceivable to integrate this solution into a vehicle; - optimality maintained compared to dynamic programming: on average 14% loss of optimality.

[0034] The description of the invention may assume a flat road or a constant gradient for each segment of the road. The impact of a variable gradient will modify the expression of the Hamiltonian. Furthermore, the invention will address the analytical solution fully constrained in torque, acceleration, and velocity.

[0035] The proposed solution is embeddable in real time, which allows it to be applied to a vehicle with computing resources close to those already available.

[0036] Prior art solutions for reducing energy consumption (eco mode, eco-driving training) currently offered generally rely on lowering the average driving speed and therefore resulting in a delay compared to the initial travel time. The invention makes it possible to minimize energy consumption for a given average speed in order to guarantee a timely arrival for the user.

[0037] In particular, the vehicle dynamics model is defined according to Newton's second law: 00 =v(t) 0^)=^(^(0-^(0) (1) (2) Or 5 is the position of the vehicle (in m); v is the speed of the vehicle (in m / s); 1 is the time (in s); m is the total mass of the vehicle including the inertia of rotating parts (in kg); the force resisting the movement of the vehicle being: Fr( 0 = 00+¾ 002 (3) Or = â + mg sin(00) is 'a rolling resistance and slope resistance (in N); ai is the rolling resistance (in N / (m / s)); 8 is the acceleration due to Earth's gravity (in m / s2); 0 is the slope of the road (in rad); a2 is the aerodynamic resistance (in N / (m2 / s2)) the tensile force being: FM=^ (4) Or Rt is the transmission speed ratio; T is the engine torque of the vehicle (in Nm); rtîre is the radius of the wheel (in m). The vehicle's speed can be deduced from the engine speed (V in rad / s):

[0038] In order to solve the eco-driving problem analytically, the vehicle dynamics are simplified as follows: v(t) = p( / )T( / ) -uh(t) -cQ + c2v?- + (6) Or 5 is the position of the vehicle (in m); v is the speed of the vehicle (in m / s); f is the time (in s); _ 7¾¾ is a variable associated with the vehicle's speed ratio, which is P — mrlire provided by a rule-based strategy that depends on the vehicle's speed, acceleration or torque setting, or the road gradient, or a combination of these elements; the demand or the slope of the road or any combination thereof; is a coefficient indicating the efficiency of the vehicle's transmission; ^gb is a coefficient indicating the efficiency of the vehicle's gearbox; Rt is the transmission speed ratio; RGB is the selected current speed ratio; m is the mass of the vehicle in kg; 1 tire is the radius of the wheel (in m). T is the engine torque control of the vehicle (in Nm); ub is the braking command (in m / s2); Co — üq! m ; aQ — at + mg sin^s)) is the rolling and slope resistance (in N); a is the rolling resistance at zero speed (in N); 6 is the slope of the road (in rad); ci is the rolling resistance of the vehicle (in N / (m / s) / kg); (2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2) / kg); vi is a velocity value (in m / s) chosen so that the dynamics model and the energy consumption model are linearized at the level of this velocity value; The energy consumption model is also adapted through simplification: Or Pr is the power drawn from the vehicle's fuel tank (in W); is the lower heating value of the fuel (in Ws / g); ^r,o is a coefficient expressed in g / s; 2½ is a coefficient expressed in gs / rad2; ^•,2 is a coefficient expressed in g / rad; is a coefficient expressed in g / (rad.Nm); ^-,4 is a coefficient expressed in g / (Nm.s)

[0039] In addition, the M3 optimization module is configured to solve the equations following: A / xx (10) min L (L(T, v) +^) dt according to s(t)=v(t) (11) v(t) = p(t)T(t) -uh(t) -c0 + - (2^ / + q) (12) =¾ (13) s(if)-Sf (14) v(tf>)=vQ (15) ^Vmax (17) " ^min — & ( Umax (18) O^ub(t) <ubmax (19) Q <T(t)<Tmax (20) pitje^p? (21) Or L is the instantaneous energy consumption of the vehicle (in W); P is the penalty that prioritizes travel time over energy gain; ,yo, V are the initial and final position constraints; vo, vf are the initial and final velocity constraints; vmin, vmax are the minimum and maximum speed constraints; amtn^ aimx are the minimum and maximum acceleration constraints; ut>max is the maximum braking constraint; Tmax is the maximum engine torque constraint; P^ Pp • • • ' P;v„,,sonl coefficients relating to a set of vehicle speeds vw(p) 9U' indicate when to change from one speed ratio to another

[0040] The parameter P may be a penalty obtained according to the prior art, but is preferably calculated according to a preferred variant detailed below.

[0041] The penalty P is used to influence travel time. This parameter has proven in the past to be complex to calibrate. The solution proposed here facilitates its calibration because it establishes the relationship between the impact of P on the average cycle speed and the average energy expenditure.

[0042] Thus, the calculation system preferably further comprises a penalty calculation module M7 having an impact on the average speed according to the equation WtDc = Uan + ap! + a^ £ with V - ^ref + C where, WtDc is the average fuel consumption per kilometer and ^ref is the average speed of the original driving cycle (in m / s) e is a parameter to be calibrated in order to achieve the desired travel time (in m / s) üq = â + mg sin^s)) is the rolling and slope resistance (in N) ai is the rolling resistance of the vehicle (in N / (m / s) a2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2)

[0043] Therefore, in the case where the average fuel consumption per kilometer is minimized, the minimum of WtDc allows us to deduce a law of P according to the average speed: dWtDc _ n _ 1-4, / :---2 a2v) (33) dv “UP ~ P

[0044] The acceleration constraints must be translated into input constraints to be applied to the model. More precisely, the strongest constraints must be taken between the braking limits and the acceleration limits of the vehicle. This is done as follows: ^brjnin — “ ^o) T (35) * max * maxi py

[0045] The final element to consider is the feasibility of the input constraints with respect to the segmented points between two sections. In some situations, these two parameters may not be compatible, and therefore the corresponding point between two sections must be adapted. This is done by using the analytical solutions for velocity and position to define an appropriate final time and distance for the current road section.

[0046] Unlike dynamic programming, which allows the consumption term to be used directly in its algorithm, Pontryagin's minimum principle minimizes at each instant a Hamiltonian H that represents the instantaneous cost of L and the weighting of each dynamic of the problem. This is implemented by the determination module M4.

[0047] In particular, the determination module M4 is configured to minimize the so-called Hamiltonian function: H = L (u, v) + / 5 + v + .1.4' (22) The variations in co-states, weighting each dynamic, are calculated as follows: ^.= -^=0 (23) 'as Ub(t) = And (24) vay The optimal, unconstrained braking control is then deduced: 4^=0 (25) dub And §=0 (26) and the optimal braking control constraint is also preferably deduced according to: 0, if Àv < 0 (27) ^bjfnax> If 0 and the optimal motor torque control constraint is also preferably deduced according to: [ Tmax, if y^ > 0 (28) 7X0*= | If W} = 0 0, if < 0 Or with -0; and ^2^^(2^2^1)^- ; being a singular couple control defining an AO constant speed phase such that ; ;aJ72^(0+Oo) ; 2c'+ 2zlhlyr^ 2c2vt) In particular, the system of equations described is ultimately defined as follows: x = H(t) X / ) (29) x = {5, v, 1, A / (30) M sit^Kta H b if your <t<th 1 ' Hk sitk.}ït <tk U \hk sitK.i <t<tK = tf (36)

[0048] Preferably, the calculation system further includes an average speed calculation module M5 over a horizon taking into account information on speed limits, obstacles, and traffic as a function of distance, preferably with a margin on this speed. This is done in particular in a step S2.

[0049] We assume that knowledge of the horizon allows us to access speed limits, obstacles, and traffic as a function of distance. Combining these elements then allows us to define the speed limit as a function of distance and to deduce an average speed over the entire horizon, called Vref.

[0050] Reference Q1 relates to iterations, references RI and R2 relate respectively to "yes" and "no" answers to the questions corresponding to references Q1 and Q2. References S and E designate respectively a start and an end of method.

[0051] It is possible to add a margin to this average speed using a parameter e. This is done in particular in a step S3.

[0052] Next comes the calculation of the penalty P detailed above, in particular in a step S4.

[0053] Next comes the calculation of an optimal cruising speed in particular in a step S5.

[0054] The absence of aerodynamic drag in the vehicle's acceleration dynamics can lead to an optimal speed that underestimates the energy savings from a lower speed. Furthermore, eco-driving trajectories resulting from dynamic programming tend to include a constant speed phase, below the maximum permitted speed, which would induce significant energy savings. For these reasons, the optimal cruising speed can be defined according to minimizing energy consumption per kilometer.

[0055] Thus, according to one aspect, the calculation system further comprises a module for calculating optimal cruising speed M8 according to the equation vopKc = arg min --½--- (32) Or, a), T is the engine speed and torque associated with the speed V (in rad / s and N / m); V is the speed window used for the search (in m / s); M-^w, T) is the engine fuel consumption map; is the scaling factor associating the time penalty with the optimal constant speed and zihv.

[0056] Next comes a division of the problem into several sections, in particular in a step S6.

[0057] In the case of an application on a driving cycle, it is proposed in the invention to first divide the optimization problem into several segments according to the distance where the maximum speed is constant.

[0058] Next, stops can be defined by a single point between two sections where the speed limit is zero. Finally, preferably, if a sequence of several speed limit sections involves acceleration or deceleration beyond the values ​​defined for the vehicle, then the intermediate section is omitted.

[0059] The initial speed of a section corresponds to the final speed of the previous section.

[0060] The final speed defined for each section corresponds to the limit speed of this section.

[0061] Next comes an association of sections with driving modes, in particular in a step S7.

[0062] Reference Q2 relates to determining whether or not a target travel time assumption has been met. If not, a step S9 is taken, which consists of adjusting the value of the margin parameter €.

[0063] Modules M9-M12 corresponding respectively to steps S6-S9 can be provided for the implementation of these steps.

[0064] If the calculated travel time is greater than the desired travel time, then the value e can be increased. This will result in an increase in P and therefore vmax.

[0065] The interaction between the system of differential equations and the multiple constraint conditions must be combined in order to find the switching times that define the sequence of driving modes in the optimal trajectories. This is done using the matrix representation (29), (30), (36) described above, which gives a time-varying linear system. A solution to the time-varying linear Hamiltonian system can be found using the exponential matrix: } (39) allowing for an analytically optimized velocity profile where Vmax — VopAc. With this procedure, different sets of analytical solutions (41) (42) (43) (44) (45) (46) can be obtained for which the unknown variables Xs>0, Xv>0, tk and tf are determined as a function of the driving mode sequence. The expressions for the speed profiles associated with each individual driving mode are then given by v — (v - fi LiZ? , (40) ^ma k ' 1 " uma,l vc = (vk - + acl vhr = (vk - ahr^y+2^ 1+ or vmax Or, fnax a>^y — c2vrc» = ^2^ ^br.l ~

[0066] In all the detailed expressions above, t = [tk i,tk), Xv(t) is the initial position co-state, the subscript "ma" represents the maximum acceleration of the vehicle, the subscript "c" represents the freewheeling phases of the vehicle, the subscript "br" represents the braking of the vehicle, the subscript "s" represents the constant speed phases of the vehicle, and vket / vk are respectively the speed state and co-state values ​​at the beginning of each driving mode. After obtaining these driving mode equations, as well as those for s(t) and Xv(t) and the expressions for the unknown variables (initial co-state conditions, switching time, and final trip duration), a complete trajectory can be calculated as a function of the specific driving mode sequence required. The final trip duration is determined by evaluating the Hamiltonian function for a final time equal to zero: Htf= = Q (47)

[0067] By way of example, the solutions to fully constrained problems are described below, that is, to scenarios for which all constraints are active simultaneously at a given point along the trajectory. The procedure and the expressions for the solutions are as follows (it should be noted that the final time of the trajectory is denoted here as tfinai).

[0068] First, the switching time ta between the driving modes corresponding to the maximum acceleration of the vehicle and the freewheeling phase of the vehicle must be found, according to: ^'max (50)

[0069] Next, Xv 0 must be determined, according to: X[5](X)= / U (51) Or, is given by the commutation function tp 1 = 0

[0070] Next, the switching time tcest is obtained with the following conditions: X[5](L) = 0 & Av = 0(52)

[0071] The remaining variables tb, tfinai, and XSj0 are finally determined using the conditions = 0; X[1J(^) = Sfetx[2](tf^ Vf

[0072] The initial co-states and switching times are then as follows, considering y = yy jE [0 L 4}: z ice.f ihv '1,1 l J

[0073] Io„( £2^)224;^ (53) Ta~ "

[0074] h = * final +

[0075]

[0080] (54) 4^17^+7.^+++0 \ , -----T-----T"---TT---“7--------7------------ +! final (c'l+2 C2 Vl) Px-tW )2)0,,,Vfÿ +)7,af'rl'-.a- fci+2c2 ( ^+2¾¼) / C j+ 2 Ca V[

[0077]

[0078] (55) (56)

[0079] ; _ P (++2 77)+2«307.»^ (>i+2q 7 )+^7^ (^2^,^) i \ p yniax I ’'Sn;L<2) (cj+2 C2 p p 1 \r^P 1 ’o ) {2 ^} +)’æc2 'n;u V° ( Or T' ;ûax p-e2 t;r-+vt-) (Cj+2 c~ vf ) ( 58 )

[0081] où, (4t) p+p{2 yKe i 17 ÿ2+y.ùe2 ¢)+6^4 +yjoe3 <î> Vn>ax)(«ù+2 c2 )) (‘"o+'^mæT'o v^+v^c^ c-, V;)) — (59) = log

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] I2r, _e | V, (^-r y..^) ( (,'■ + 2 ('.v;)‘ + ((., + 2(^.) + / , ( 2 . ((:,)-^,:)(.-. + 2(:.1,) (60) In one variant, it depends on a consumption model linking energy consumption to cruising speed. In one variant, a minimum speed is added to the calculations of the optimization module. The invention also relates to a computer-implemented method comprising steps for carrying out the actions and / or calculations of a computing system as described above. Another object of the invention relates to a computer program product comprising program code instructions for executing the steps of a computer-implemented method as described above, or steps for carrying out the actions and / or calculations of the computing system as described above, when said program is running on a computer. The program can, for example, be loaded into the memory of a computer in a motor vehicle. The invention also relates to a motor vehicle comprising a computing system as described above or a computer program product as described above.

Claims

Demands

1. A computer-implemented calculation system for determining a trajectory while minimizing the energy consumption of a motor vehicle with an internal combustion engine, the system comprising: - a dynamics modeling module (M1) and energy consumption modeling module (M2) configured to define driving parameters, - an optimization module (M3) configured to define driving constraints based on the driving parameters, - a trajectory determination module (M4) by calculations according to a Pontryagin minimum principle minimizing a so-called Hamiltonian function of said rolling parameters; characterized in that the dynamics model is defined according to the equations: 5(f)=v(0 (1) HO =p(t)T(t)-ub(t)-cQ + c2v?- + (6) Or s is the position of the vehicle (in m); v is the speed of the vehicle (in m / s); ! is the time (in s); _ f},nsbRrRgb is a variable associated with the vehicle's speed ratio P ~ Vt is a coefficient indicating the efficiency of the vehicle's transmission; Vgb is a coefficient indicating the efficiency of the vehicle's gearbox; Rt is the transmission speed ratio; RGB is the selected current speed ratio; m is the mass of the vehicle in kg; rfi>-e is the radius of the wheel (in m). T is the engine torque control of the vehicle (in Nm); ub is the braking command (in m / s2); c^a^ / m ; üq = â + mg si^^y)) is the rolling resistance and the slope resistance (in N); a is the rolling resistance at zero speed (in N); 6 is the road gradient (in rad); ci is the vehicle's rolling resistance (in N / (m / s) / kg); c2 is the vehicle's aerodynamic drag (in N / (m2 / s2) / kg); vi is a speed value (in m / s) chosen so that the dynamics model and the energy consumption model are linearized at this speed value; the energy consumption model is defined by the equation: X'''+ + zyJ z )+ + where Pr is the power drawn from the vehicle's fuel tank (in W); is the lower heating value of the fuel (in Ws / g); , RrRXb ■ ¢ = -r- ' ' 'tire yrp is a coefficient expressed in g / s; 1)-,1 is a coefficient expressed in gs / rad2; is a coefficient expressed in g / rad; is a coefficient expressed in g / (rad.Nm); Ka is a coefficient expressed in g / (Nm.s)

2. A calculation system according to claim 1, characterized in that the optimization module (M3) is configured to solve the following equations: Pf z (10 min (L(T,v)+fi) dt according to (11) v(z) = p(t)T(t)-ub(t)-c0 + c2v?- + (12) ^(^)=¾ (13) s(tf)=Sf (14) v(to)=*o (15) (16) < 17 ) -amin <a(t) <a^ (18) O^U / M <uhjnax (19) Q <T{t)<Tmax (20) P^)^{pffPv --- / ¼} (21) Or L is the instantaneous energy consumption of the vehicle (in W); ,6' is the penalty prioritizing travel time over energy gain; yo, are the initial and final position constraints; Vf are the initial and final velocity constraints; vmin, Vmax are the minimum and maximum speed constraints; am, &max are the minimum and maximum acceleration constraints; ubjnax is the maximum braking constraint; Tmax is the maximum engine torque constraint; / ¾ Pp • - •, Py^s are coefficients relating to a set of vehicle speeds p) which indicate when to change from one gear ratio to another

3. A calculation system according to claim 2, characterized in that the determination module (M4) is configured to minimize the so-called Hamiltonian function: H = Hu, v) +P + Às v + v (22 ) Or Às and Àvs are variations of co-states weighting each dynamic, the variations of co-states weighting each dynamic being calculated as follows: ;,= -æ=o (23) 5 aces and (24) y dv the optimal unconstrained braking control being preferably then deduced: fl=0 (25 and g!=0 (26 ) and the optimal constrained braking control being also preferably deduced according to: [ 0.If Av < 0 (27) lW = » KiJ >0 and the optimal motor torque control constraint also preferably deduced according to: f Tmax? If Q (28) T(t)* = Tm if = 0 | 0, if < 0 WHERE with — 0 ; and ; T a being a singular torque control a~ Md defining a constant speed phase such that _ c2vrcj z^'ta ; V^-2c,+ 4c2v, 2zlhvyr / (t) 2 2c2V / ) with finally, the system of equations described is defined according to: x = H(t)x(t) (29) x = U v, 1, 2 v} (30).

4. A calculation system according to any one of claims 1 to 3, further comprising an average speed calculation module (M5) over a horizon taking into account limit speed information, obstacles, traffic depending on the distance, preferably with a margin on this speed.

5. A calculation system according to any one of claims 1 to 4, further comprising a penalty calculation module (M7) having an impact on the average speed according to the equation WtDc-^(a + a}v+a^ ) with V=Vref + £ where, Vf-ef is the average speed of the original driving cycle (in m / s) e is a parameter to be calibrated in order to achieve the desired travel time (in m / s) — â + mg sin(0(5')) is the rolling and slope resistance (in N) a\ is the rolling resistance of the vehicle (in N / (m / s) ^2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2)

6. A calculation system according to any one of claims 1 to 5, further comprising an optimal cruising speed calculation module (M8) according to the equation . / \ (32) v^^argmmj ' J ' J where, a), T is the engine speed and torque associated with the speed V (in rad / s and N / m); V is the speed window used for the search for v°pt* (in m / s); T) is the engine fuel consumption map; z is the scaling factor associating the time penalty with the optimal constant speed and zihv.

7. Motor vehicle comprising a heat engine and a calculation system according to any one of claims 1 to 6.

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