TRAJECTORY CALCULATION SYSTEM MINIMIZING ENERGY CONSUMPTION OF AN ELECTRIC MOTOR VEHICLE AND TAKING INTO ACCOUNT COOLING PHASE OF THE VEHICLE

Abstract

The invention relates to a computer-implemented calculation system for determining a trajectory while minimizing the energy consumption of an electric motor 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, some of the computer-implemented calculation steps are performed by a motor vehicle battery management system. Figure 1

Description

Title of the invention: TRAJECTORY CALCULATION SYSTEM MINIMIZING THE ENERGY CONSUMPTION OF AN ELECTRIC MOTOR VEHICLE AND TAKING INTO ACCOUNT COOLING PHASES OF THE VEHICLE

[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 adapted for electric 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 to guarantee an eco-driving trajectory, That is, a velocity trajectory that minimizes energy consumption for the same travel time as the initial velocity trajectory developed previously. It consists of using a dynamic programming algorithm to calculate the optimal velocity 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 and real-time application 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 vehicles, particularly 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 does not take into account the vehicle's coasting phases, as it assumes a constant transmission efficiency. This impacts the overall performance and accuracy of the solution and introduces suboptimality. "Coasting phase" refers to any phase during which the vehicle decelerates solely due to its inertia, without regenerative braking. 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 subtraction. jectories calculated when the different constraints are not compatible with each other.

[0009] To overcome the shortcomings of the prior art, the invention proposes a computer-implemented calculation system to determine a trajectory while minimizing the energy consumption of an electric motor vehicle, the system comprising: - a dynamics and energy consumption model module configured 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 equation: (1) 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); The optimization module (M3) is configured to solve the following equations: . . , ™ n . , X,(M«. V ')+ / Ù * {M(r according to v(r0) = v0 (10) (11) (13) (14) (15) v(tf)=Vf <16) (17) -umin <u(t) <umax (18) -amin <a(t) <amax (47) Or £ is the instantaneous energy consumption of the vehicle (in W); / i is the penalty prioritizing travel time over energy gain; sf are the initial and final position constraints; vo, vf are the initial and final velocity constraints; vmin, ^max are the minimum and maximum speed constraints; umm, Umax are the minimum and maximum traction acceleration constraints; amm, &max are the minimum and maximum acceleration constraints; the determination module (M4) being configured to minimize the so-called Hamiltonian function: H = L(m, v) + v + / lvv (19) Or 4 and 2 are variations of co-states weighting each dynamic, L(u, v) corresponds to the energy that can be saved on the journey,

[0010] u is the traction acceleration command (in m / s2); the co-state variations weighting each dynamic, being calculated as follows: 4s=-^=o (23) A as And --(y ■ dv ' emd 't em2 ' 7 the optimal unconstrained traction acceleration command is preferably then deduced: of (25) Ultimately, the system of equations described is defined as follows: .t = H(f) XÔ (27) x = {5, v, 1, X, Ax] (28) the dynamic model is further defined according to the following equation: HO = 77^(^), / / ( / ) -c0 (6) Or = a + mg sin(X^)) is 'a rolling resistance and slope resistance (in N); a is the rolling resistance at zero speed (in N); m is the mass of the vehicle in kg; 6 is the slope of the road (in rad); is a coefficient indicating the efficiency of the vehicle's transmission; Sgn( II) provides the sign of the function u(t) and is therefore equal to -1 or 1 when u(t) is non-zero; L(il, v) can then be expressed according to the equation: L(w, v) ^y eml v(>) +^”( H )y? u(t) v(t) «(O 2 (22) Or ^emA represents friction losses (in W / (m / s)); ^em.2 represents the equivalent mechanical power (in W / (m2 / s3)); P em.3 represents the ohmic losses (in W / (m / s2)2); The energy consumption model is defined by the equation: Or P b is the power drawn from the battery (in W); P aux is the power consumed by the auxiliaries (in W); Pm is the electrical power consumed by the machine (in W) such that: PmU HO + y mC v(0 + y eri0 bed} 2 (9) the optimization module (M3) being further configured to solve the equation next: v(0 = ?j t s ^ u Ku{ r) -c0 (6) and the optimal traction acceleration control constraint is also preferably deduced according to: SI Ua Umax SI 0 Ua < Umax if Ua < 0 & Ud > 0 si -umin <ud<Q (26) if u d < -u min

[0011] 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.

[0012] By taking into account the vehicle's freewheeling phases (particularly thanks to the presence of the coefficient and the function sgn(u) in the dynamic model), the calculation system is more accurate than prior art calculation systems (and therefore more efficient in terms of minimizing the vehicle's energy consumption). Indeed, unlike prior art calculation systems, which assume constant transmission efficiency during the two operating modes of the electric machine (traction mode and regeneration mode), the calculation system according to the invention takes into account the fact that the traction acceleration Ax,t(t) is divided into two terms according to the equation: Axj(t) (48 ) This impacts the vehicle dynamics model and leads to a more precise analytical solution. The proposed invention also provides 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 the calculation of an eco-driving trajectory to be integrated into an automotive computer or a mobile phone application, for example. Furthermore, the proposed invention makes it possible to determine the vehicle dynamics based on parameters accessible to a corresponding vehicle's battery management system, to obtain a theoretical optimization of the route, and to to allow for route determination with simplified calculations, limiting processor calculation time.

[0013] 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.

[0014] According to one variant, the calculation system further includes a penalty calculation module having an impact on the average speed according to the equation ^ / ^ = ^(^ + (2^ + (22^ + | (29) with 9 ~ ^ref + C where, 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) a> is the rolling resistance of the vehicle (in N / (m / s) a2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2)

[0015] This helps to limit errors in calculating journey parameters, in particular journey time.

[0016] According to one variant, the calculation system further includes a module for calculating optimal cruising speed according to the equation v oph; = arg min y Or, T is the speed and torque of the electrical machine associated with the speed V (in rad / s and N / m); V is the speed window used for the search (in m / s); M^îo, F) is the map of the energy consumption of the electrical machine; - is the scaling factor associating the time penalty with the optimal constant speed.

[0017] 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.

[0018] 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. M^&,T)z+P (31)

[0019] The method can be implemented in an automotive vehicle battery management system.

[0020] 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.

[0021] The program product can be loaded into the memory of a motor vehicle battery management system, serving as a computer.

[0022] The invention also relates to a motor vehicle comprising a computing system according to the invention or a computer program product according to the invention.

[0023] 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.

[0024] 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.

[0025] More specifically, the invention proposes a computer-implemented calculation system to determine a trajectory while minimizing the energy consumption of an electric motor vehicle.

[0026] 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.

[0027] 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.

[0028] By taking into account the vehicle's freewheeling phases, the invention is more accurate than prior art calculation systems (and therefore more efficient in terms of minimizing the vehicle's energy consumption). Furthermore, The invention significantly reduces the computing power, processing time, and memory required to generate an eco-driving trajectory; and maintains near-optimal performance compared to dynamic programming calculations, respecting the travel time constraint while offering reduced fuel consumption compared to the original (non-optimized) cycle. The invention thus allows this type of algorithm to be integrated into an automotive computer or a mobile phone.

[0029] 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.

[0030] 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 3% loss of optimality, which represents a clear improvement compared to the solution described in patent document FR 3 124 147 Al (12% on average loss of optimality compared to dynamic programming).

[0031] The description of the invention may assume a flat road or a constant road gradient for each segment thereof. The impact of a variable road gradient will modify the expression of the Hamiltonian. Furthermore, the invention will deal with the fully constrained analytical solution in torque, acceleration and velocity.

[0032] 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.

[0033] 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.

[0034] In particular, the vehicle dynamics model is defined according to Newton's second law: (1) < / ) -F^t) ) (2) Or  is the position of the vehicle (in m); v is the speed of the vehicle (in m / s); z 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(t) = «o + tij v(t) + a2 XO2 (3) Or aQ — at + mg sin(0(.y)) is the rolling and slope resistance (in N); is the rolling resistance (in N / (m / s)); S 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: Or Rt is the transmission speed ratio; T is the torque of the vehicle's electric machine (in Nm); 1 tire is the radius of the wheel (in m). The vehicle's speed can be deduced from the speed of the electrical machine (0 in rad / s): v(0 = "XQ'",,. (5)

[0035] In order to solve the eco-driving problem analytically, the vehicle dynamics are simplified as follows: t) -c0 (6) Or is the efficiency of the transmission; Sgn ( U ) provides the sign of the function u(t) and is therefore equal to -1 or 1 when u(t) is non-zero; Cq “ CIq / ni * = â + mg if 11(^5)) is the rolling and slope resistance (in N); 6 is the slope of the road (in rad); w is the traction acceleration command (in m / s²) such that: < 7) \ 7 ni i!;,e The energy consumption model is also adapted through simplification: P,,(r)=P m (z)+P o „. (8) OR P1 is the power drawn from the battery (in W); P aux is the power consumed by the auxiliaries (in W); Pm is the electrical power consumed by the machine (in W) such that: P,n(u, v) = V emA +y em2 m(?) v(r) utf (9) Or Pem,i represents friction losses (in W / (m / s)); ^em,2 represents the equivalent mechanical power (in W / (m2 / s3)); Yemj represents ohmic losses (in W / (m / s2)2). In addition, the M3 optimization module is configured to solve the following equations: min {hG'MXX dt (10) according to (H) v(f) =^tssn^uku(t) -cQ (6) ^(^)=¾ (13) (14) v( / 0)=v0 (15) vÇtf^=Vf (16) (17) -umin <u^ (18) -amin <a(t) <amax (47) Or £ is the instantaneous energy consumption of the vehicle (in W); P is the penalty that prioritizes travel time over energy gain; 5o, Sf are the initial and final position constraints; vo, vf are the initial and final velocity constraints; vmax are the minimum and maximum speed constraints; umm, Umax are the minimum and maximum tensile acceleration constraints; amin, ^max are the minimum and maximum acceleration constraints.

[0036] It should be noted that in order to facilitate the derivations of certain analytical expressions, the effects of transmission efficiency (translated by the term ^ '«>'(«) in equation (6)) are transferred from equation (6) to equation (9).

[0037] Equation (6) then becomes equation (6') according to: v(z)=w(0-Q) (6') and equation (9) becomes equation (9') according to: v) =yeml v(z) +v-^Yy v(t) ' x em,3

[0038] The parameter fi can be a penalty obtained according to the prior art, but is of preference calculated according to a preferred variant detailed below.

[0039] 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.

[0040] Thus, the calculation system preferably further comprises a penalty calculation module M7 having an impact on the average speed according to the equation WtDc = + + + | 'h 0 1 / • with 3' ~ Vref + C where, WtDc is the average kilometer consumption, ^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) = « + mg sin( / ?(5')) is the rolling resistance and the slope resistance (in N) is the rolling resistance of the vehicle (in N / (m / s) a2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2)

[0041] Therefore, in the case where the average fuel consumption per kilometer is minimized, the minimum of WtDc allows us to deduce a law of according to the average speed: dWtDe _ n_ A^i+2 a2v) (30) Jv — VP —

[0042] 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 traction acceleration limits and the vehicle acceleration limits. This is done as follows: amm - C0) (48) ~ inin(wHWM-, ^intax Q>) <49>

[0043] The last element to consider is the feasibility of the input constraints with respect to the segmented points between two segments. In some situations, these two parameters may not be compatible, and therefore the corresponding point between two segments 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 section of road.

[0044] 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.

[0045] In particular, the determination module M4 is configured to minimize the so-called Hamiltonian function: H - L ( u, v ) + fi + v + (19) where L(u, v) is defined according to an integral of the instantaneous consumption along the path, considering only the power from the electric machine: Jf rO' J = ] tn (L(ik v) + p) dt = ] tn (P m (u, v) + 0) dt (20) so as to deduce L(u,v), L(u)=b3(u(t)-c0)2 + b^02 ( ) The variations in co-states, weighting each dynamic, are calculated as follows: ; = =() ds v (23) And . + u(t)+k\ v dv em.l U em2 / (24) The optimal unconstrained traction acceleration command is then deduced: of (25) and / or the optimal traction acceleration command is then deduced: '^mûv SÎ 0 < lla Umax if Ua < 0 & lld > 0 siud<-umin (26) In particular, the system of equations described is ultimately defined as follows: (27) (28) H sit Q <t<t a (32) H b if t a <t< t h Ht = \ u H k sit k _^t <t k U \ h k sir K^ <t<t K = t f

[0046] Five distinct optimal input modes are thus obtained for the traction acceleration control u(t): a mode where u(t) = Umax ' a mode where u(t) = ; a mode corresponding to a phase of acceleration of the vehicle and given by the expression of ua in equation (26) above; a mode corresponding to a phase of coasting of the vehicle and in which the traction acceleration command u(t) is zero; and a mode corresponding to a phase of deceleration of the vehicle and given by the expression of ud in equation (26) above.

[0047] 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.

[0048] 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.

[0049] 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 beginning and an end of Mx(&T)z+0 (31) method.

[0050] It is possible to add a margin to this average speed using a parameter €. This is done in particular in an S3 step.

[0051] Next comes the calculation of the penalty P detailed above, in particular in a step S4.

[0052] Next comes the calculation of an optimal cruising speed v°p^ in particular in a step S5.

[0053] 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 v°ptc can be defined according to minimizing energy expenditure per kilometer.

[0054] Thus, according to one aspect, the calculation system further comprises a module for calculating optimal cruising speed M8 according to the equation v opT , c = arg min Or, T is the speed and torque of the electrical machine associated with the speed V (in rad / s and N / m); V is the speed window used for the search (in m / s); MY(d), T) is the map of the energy consumption of the electric machine; is the scaling factor associating the time penalty with the optimal constant speed.

[0055] Next comes a division of the problem into several sections, in particular in a step S6.

[0056] 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.

[0057] 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.

[0058] The initial speed of a section corresponds to the final speed of the previous section.

[0059] The final speed defined for each segment corresponds to the limit speed of this section.

[0060] Finally, the cod term in the simplified model can be updated at the level of each point between two segments such that: (33) Or, v, = mam vn, min(v, )) @4)

[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 e.

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

[0064] If the deduced travel time is greater than the desired travel time, then the value e can be increased. This will result in an increase in |3 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 (27), (28), (32) 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: X ( tf) = Shk( ) .., x(^ (35) allowing for an analytically optimized speed profile where vmax — VopLc. With this procedure, different sets of analytical solutions 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 vma = ( - c0 + umax ) t + vk (36) va = <W2 + + vk vc = cot+vk (38) vd - ad,\t2 + a^t + vk (39) Vmd = ( -Cn-Umin)t + Vk (40) hî ^max (41) Or, v _ (42) ™a,l 4y , 'em.y (43) ^.2 = ---- ---~ 'ent^ (44) adA =----------4F^-- _ (45) a^2 ^,,^,2

[0066] In all the detailed expressions above, t = [tk i,tk), XSjO is the initial position co-state, the subscript "ma" represents the maximum acceleration of the vehicle, the subscript "a" represents the acceleration of the vehicle, the subscript "c" represents the freewheeling phases of the vehicle, the subscript "md" represents the maximum deceleration of the vehicle, the subscript "d" represents the deceleration of the vehicle, the subscript "s" represents the constant speed phases of the vehicle, and vket Xv>ks 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 journey time), a complete trajectory can be calculated as a function of the specific driving mode sequence required.The final duration of the journey is determined by evaluating the Hamiltonian function for a final time equal to zero: . Htj = — Q (46)

[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 for the input constraint must be found. maximum according to:

[0069] xM 40) & uM ra 0A 1 M _ ^(ÎO); 'em,3 ernS

[0070] Next, the entry point for the speed limit must be determined to find tbet / . v0, according to:

[0071] x(t h )=e H ^-t a ) } x(0) et uti liser ^[2] (^) = & x [2] (4) = 0 (51)

[0072] To define the exit point, the state evolution must be extended up to td of such so that:

[0073] H / x £6™(l) (52) and use x(t d ) ~e H A)e h n ex(0) 'kon V / x _ n (53) during the rolling phase in Yÿ , U,U, -y- X{td) - U freewheeling to find tc

[0074] The following driving mode must then be used to find the start of the freewheeling mode, according to:

[0075] } KM (54) x(t e )-e H ^^^ a ' d c 'e H ^^h)eex(0) find f] with / x _ [n ^« »,2 nn / \ n (55), which defines the MVe / — HA 2«y ' • 2»2y ~ 1 'i ' 3 • / l 3 End of freewheeling mode

[0076] The final driving mode in the sequence is related to the minimum input; therefore, the starting point of this constraint must be used to find te, according to:

[0077]

[0078]

[0079] (56) x(tf) -e H d['r',}e '' d eex(0) and take m \ [ '>'„„2 "U / ) = L 'r 1 em.3 0,0, U • (57) Next, we need to impose xpj ( tfinal) = Vf ^ans 'c find 'c time of com mutation tf, knowing that: (58) tfnatif May. ta) ex(0)

[0080] Finally, we need to use the conditions H.finai — 0 and x [1] (? final) = Sf To determine X s>oet tfinai, respectively, according to:

[0081] H / w = +¾ <59' °ùr"cl so“des matrices related to the Hamiltonian function H

[0082] The initial co-states and switching times are then as follows: J _ V«™+F„,2 Co 7 (60) ^SO « 2 v flt l>iUÏX c <r Vi)+P Vt2 Vmax T® Tl,2 m2 C0 Tf Vt J)

[0083] _ Ven# W V,1 nt2 v<r2 cn «max Vmax (62) ( Lm.î C<f+^ )

[0084] Vfncix~ vwax~P U fi Venté l'{max ^max (63) b ( Vem3 c^P > 12) (ctrunmx)

[0085] _ / fl2 <0 F 'l,^. P 'XV W fi r02 Fma P l?7 'if+l «W / ¾2 P? VmiTmî“y 10 -¾ A c»^2 \ (co+“mn)

[0086] C«SW%,U C04 ^3rem3+yemj Vanx 'l, ¢ / F^F^*»» c03 g? vmax <Q3 V, Vem3 \ . ( ‘W,„m) ( rcm,3 n,2) (ycm.3 c)<ArclIt2 vmM > wx c0 vf-P fi fi ) / • ma

[0087] / fi y 4 Vnü}x-Vj fi ^+3 fi fi fi y^T, tinax'*2 Vf P Cq- .fi fi p^2 ,6' Ço fi~ Pmax-'+p'^ ? V / fi f-'o fi fi 3 fi CQ fi fi ^niax“F€îr!#2 vf fi Q) vmax \ (cq+h,,^) ()3,,,,3^0^¾2) ()'cm-3 fi fi)

[0088] 2 P C0 Tir Lm.3 “min V™^P Vr Lm,3 “»>in2 ^,5 “mm P “min >^^2 VnBX ..............................................................................■■■■■;.....................................................................................................;............................ + ( ^u+WnUn 1 ( F«m3 C0^ ,) ( Lm.3 ^eaU vm« C0 V%o2 v™« C0 lli+!j J

[0089] ( co+«min ) ( Lm,3 ) ( Fans ,¾2¾2 ™x '3! 'Wx C0 fit+P fi2 )

[0090] ?'em.3~ vmax+co" huax^ 9 ^&m3 ^min}'em2 eni,3 ^max“ \ ( c0+um^ ) ( F,^ Cir+P Tl2 ) ( LnV3 ^F^ Van» c0 fl,2+>fim2 V^- ^r+P ) 7 (64)

[0091] _ / fi2 Cp fifi+n^ fi2 fi 'V >1 fi Vgffi cfi fifi+ir,,3 V«M fi (V fifi+2 “mmfi r:fi fi? rmiTmi »W fi '2 M»3⁄4 ​​P d **»\» CO ' (XmVfVfifi?)

[0092] 7Vmox r04 ' ^111,3^01.2 VrnûX r04 l'KGt:i r0'' u{lf,a Hoax Qp (''a+^mai) (^,3⁄42^3⁄42) {3] / x1X20^03™fi 7>- vniax“''f fi '-il" '1~ 7'em,3 1 / 7eni3“Fôm2 fi ''Û X?'fi cû}i^ fi Lû fi fi ^iiiax^'^u^ fi '-fi fi '"max \ ( Co+Xnù ) ( Fjxx « I <-j' >?\?-rt ) )

[0094] P 'ffi 'tV T? "»a WtTa^ v Vr,,„r+)'„s '7 G? 1? >mlJ '7 '!, T^j 'àit^-a2 '>* r^1 k'^,+' 1 1 . ()'„,,3f o-^,,,2' »«x QO7,a,„„ 1 (65)

[0095] L— 1 / a / > • „ , \ ) tfinale + \ ( ) ( reltt3 Co-f CM co Vmax Cq 11,2 ) 7

[0096] £23M^L1222ïI2i2™é222ZL19^^ (66) ( co+“IflJn ) ( L™.3 c02-FBm,2 'WQ) fl^+V^ Vmax 0) >1,+$ ^2)

[0097] / ''mn C02 fp+Vml 'rnax Cyfiry^Cg2-}'^ 'Wx <0 rp+fic(> Vm» c0 *1,+$ «rai:, V,2 \ ff~\ < 3 i 3 0 aï ' final+ \ L(Mn,D) (rem3q>-%,tü''maxQ>^3+ia,.21™^ ! ' ,

[0098] P VfP t?,2 ^+¾)2 ^„.3 >1, V W2 Cp 3* «min 'UX^ Vf V^a ( ^tf+Wn™ ) ( nm,3 '+>'« '+™ C0 ) (67)

[0099] _ / L',0,j+A7+ / ,(-77,) / ,,2+07:+) / ,,2 / 3) v„,(^7,3,,,2+07 / +^2)6) ^+(+,,,2+0^7,2) (or"»™) 3 \ t final ~ ------' ' : ---------------~2 ----------------------------------------------------~2 ' vf‘ \ 6+,,¾ ( <i «,m) 1) ^- +^^ (-fl+w) () ,3 +-) ,,2¾^                                         +

[0100] / - / .+.¾¾¾¾¾.) 2¾.)¾¾¾¾) 12 / ,,. / / 2^, / / ¾.)8)¾^ „, LJ 6+,,...( / / 1- / ,,.) (¾. l+r.-"n„-) U. / ,, / / ,, ^,U,.a,) (3...,-- / / ^72) [C.,-H..„.) { rm (68)

[0101] where the term aev is obtained using software specialized in symbolic calculations

[0102] In one variant, ^p1 depends on the power of the battery with auxiliaries included, or any other consumption model linking energy consumption to cruising speed.

[0103] In one variant, a minimum speed is added to the calculations of the optimization module.

[0104] 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.

[0105] 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.

[0106] The program can, for example, be loaded into the memory of a battery management system of a motor vehicle, serving as a computer.

[0107] 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 an electric motor vehicle, 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; The dynamic model is defined according to the equation: (1) Or 5 is the position of the vehicle (in m); v is the speed of the vehicle (in m / s); ' is the time (in s); The optimization module (M3) is configured to solve the following equations: min (io ) according to *(0=0 (11) (13) (14) (15) Vmin <v(t) <Vmax <17) -umin <u(t) <umcK (18) -amin <a(t) <amax (47) Or L is the instantaneous energy consumption of the vehicle (in W); is the penalty that prioritizes travel time over energy savings; yo, sf are the initial and final position constraints; vo, V f are the initial and final velocity constraints; vmin, Vmax are the minimum and maximum speed constraints; umm, ^max are the minimum and maximum acceleration constraints; amm^ amax are the minimum and maximum acceleration constraints; the determination module (M4) being configured to minimize the so-called Hamiltonian function: H = L(m, v) v + 2vV (19 ) Or and 4 are variations of co-states weighting each dynamic, L(u, v) corresponds to the energy that can be saved along the path, 11 is the traction acceleration command (in m / s2); the co-state variations weighting each dynamic, being calculated as follows: ^=-^=0 (23) And +„-^(«)yw(r)+xJ (24) 1 dv ' em,L 't ' em 2 ' / the optimal unconstrained traction acceleration command is preferably then deduced: ) Ultimately, the system of equations described is defined as follows: X = H(f) x(t) (27) x = {.v. v, 1, Às, (28) characterized in that the dynamics model is further defined according to the following equation: v(t) _Cq (6) Or c0-aQ / m; üq = â + mg sin(3(s)) is the rolling and slope resistance (in N); a is the rolling resistance at zero speed (in N); m is the mass of the vehicle in kg; 0 is the slope of the road (in rad); is a coefficient indicating the efficiency of the vehicle's transmission; Sgn ( ll ) provides the sign of the function u(t) and is therefore equal to -1 or 1 when u(t) is non-zero; L{ u, v) then expressing itself according to the equation: Uu, v) = y^ u(t) v(z) ^2 Or YemX represents friction losses (in W / (m / s)); Vem.2 represents the equivalent mechanical power (in W / (m2 / s3)); Vem.3 represents the ohmic losses (in W / (m / s2)2); The energy consumption model is defined by the equation: Pb(t) = Pm(t) + Pma. (8) OR P h is the power drawn from the battery (in W); P aux is the power consumed by the auxiliaries (in W); Pm is the electrical power consumed by the machine (in W) such that: Pm (u, v) = yeml v (t) + yemu (t) v (t) + yem3 u(ïf (9) in that the optimization module (M3) is further configured to solve the following equation: (6) and in that the optimal constrained traction acceleration command is also preferably deduced according to: — Umax (26) ua = --^—Àv(t) - y"""-y(^), siQ <ua<umax ~ ■ 0, si ua£ 0 & udZO A-(0 - 2nr v(t), si-umin<ud<0 i ' { em3 , SI Uj — ~Umjn

2. A calculation system according to claim 1, further comprising an average speed calculation module (M5) over a horizon taking into account information on speed limits, obstacles, traffic as a function of distance, preferably with a margin on this speed.

3. A calculation system according to claim 1 or 2, further comprising a penalty calculation module (M7) having an impact on the average speed according to the equation WtDc = -^(a0 + a [P+a2v2^ + f (29) with V = Vref+ £ where, Vref 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) a0 — a + mg Sin(fX sj) is 'a rolling and slope resistance (in N) ûi is the rolling resistance of the vehicle (in N / (m / s)) a2 is the aerodynamic resistance of the vehicle (in N / (m2 / s2)

4. A calculation system according to any one of claims 1 to 3, further comprising a module for calculating optimal cruising speed (M8) according to the equation v^argmin - J ÎJ v / where, w, T is the speed and torque of the electric machine associated with the speed V (in rad / s and N / m); V is the speed window used for the search for v°pfp (in m / s); T) is the energy consumption map of the electric machine; z is the scaling factor associating the time penalty with the optimal constant speed.

5. Electric motor vehicle comprising a calculation system according to any one of claims 1 to 4.

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