Research on active vehicle obscurity based on model predictive control

Abstract

Driverless vehicles interacting with other traffic participants, such as cars, pedestrians and bicycles inevitably will inevitably interact in complex traffic environment. During the interaction, all potential collisions must be avoided to ensure driving safety. Based on the model predictive control, this paper analyzed the active obstacle avoidance algorithm for unmanned vehicles, and proposed a collaborative trajectory planning program for unmanned vehicles with multiple collision and collision management. The coordinated collision avoidance rules based on angle change were used to solve the consistency problem of distributed collision avoidance. The simulation results show that the scheme can effectively solve the multiple collision problems between UAVs.

Keywords

Model predictive control unmanned vehicle active obstacle avoidance algorithm collision control

1 Introduction

Unmanned vehicles will inevitably interact with other traffic participants such as cars, pedestrians and bicycles while traveling in complex traffic environments. All potential collisions must be avoided during the interactive process to ensure driving safety [1]. In order to accomplish this task, we need the driverless vehicle to accurately detect and track the dynamic obstacles and estimate their motion state. Secondly, different kinds of dynamic obstacles have different movement characteristics. To improve the reasonableness of the collision avoidance behavior, Identify the types of dynamic obstacles for driverless cars to perform more reasonable collision avoidance behavior [2]; finally, in order to avoid potential collision with dynamic obstacles, require unmanned vehicles to accurately predict the dynamic obstacles Motion trails, especially dynamic vehicles with fast motion. However, the existing methods based on single contour feature have low accuracy and speed in dynamic obstacle detection and tracking, which cannot meet the requirement of dynamic obstacle avoidance safety [3], dynamic obstacle based on contour feature and motion state The accuracy of object recognition algorithm is low and its recognition scope is small, which cannot meet the requirements of driverless collision avoidance rationality. The trajectory of dynamic vehicle is determined by many factors. The existing trajectory prediction method error based on the real-time motion state of dynamic vehicle Larger, does not meet the requirements of collision avoidance accuracy of driverless cars [4].

2 State of the art

Dynamic obstacle detection and tracking are the prerequisites for driving a driverless car in a real traffic environment. Driverless cars can detect and track moving objects such as cameras, millimeter-wave radar and laser radar through different sensors [5]. Thanks to the rapid development of computer vision, researchers have proposed many excellent performance camera-based dynamic target detection and tracking methods. The camera data contains abundant information of the obstacle texture. The extracted features can well accomplish the obstacle association, However, due to the high light intensity requirements of the camera, the light is weak or too drastic changes will result in failure of the camera-based dynamic obstacle detection method, in addition the camera cannot provide accurate position information of the obstacle will result in the error of the motion state estimation results Large, in order to overcome these two shortcomings of the camera [6], the researchers used a stereo camera and an infrared camera. The stereo camera can provide the position information of the obstacle but its detection field of view and the detection range are small. The infrared camera is affected by the light conditions Small, but its resolution is low. The millimeter-wave radar is sensitive to the longitudinal motion of the dynamic target and has a long detection range. It can be used in the advanced auxiliary driving system to accomplish such actions as adaptive [7]. However, due to the structural limitations of the millimeter-wave radar, the detected dynamic the target lateral motion data is inaccurate and its sensing visual field is narrow, which cannot meet the need of dynamic obstacle detection and tracking of driverless vehicles. Lidar can obtain the accurate position of dynamic obstacles with little influence of light intensity, which is an ideal environment perception Sensors, the current driverless vehicle detection tracking the use of information mainly from the laser radar.

3 Methodology

3.1 DMPC principle

MPC is a control strategy based on on-line optimization. At each sampling moment, MPC predicts the future output of the system based on the historical information and future input of objects in finite time-domain, and optimizes the future of the object through a certain performance index Control the input, solve an open-loop optimization problem, get a control sequence, and apply the first control of the control sequence to the controlled object. At the next sampling moment, the new state measurement is used to re-solve the open-loop optimization problem to form closed-loop control. Predictive control at each moment has a relative to the moment of performance indicators, can effectively overcome the model inaccurate, time-varying and other factors, with strong robustness. For the implementation of MPC, it is divided into 2 types: centralized and distributed. However, as the number of unmanned vehicles increases, the input variables increase linearly and the solution complexity increases, and the traffic volume increases dramatically in a nonlinear manner. Because the dynamics of each UAV are decoupled from each other, each UAV can independently control unmanned vehicles through independent constraints and status conditions. In the process of collision avoidance, the unmanned workshop exchanges information with each other through intermachine communication equipment to cooperate with each other, so it is suitable for using DMPC structure to control he DMPC structure of multi-UAV distributed coordinated collision avoidance needs to solve two key problems: prediction model and rolling optimization mechanism.

3.2 Unmanned aerial vehicle (UAV) motion model

Define the unmanned vehicle formation as V unmanned vehicles = {unmanned vehicles i | i = 1,2,…, N unmanned vehicles}, O is the origin of the selected coordinates, Ox points to the north, Oy axis points to the east, The Oz axis is determined by the rule of the right hand. Initial t0 time, UAV initial state vector is x_i (t₀) = [x_i (t₀), y_i (t₀), φ_i (t₀)] ^T. Assuming that all UAVs move within the horizontal plane Oxy, their particle motion model can be expressed as:

$[\begin{matrix} {\dot{x}}_{i} (t) \\ {\dot{y}}_{i} (t) \\ {\dot{φ}}_{i} (t) \end{matrix}] = [\begin{matrix} v_{i} (t) \cos φ_{i} (t) \\ v_{i} (t) \sin φ_{i} (t) \\ ω_{i} (t) \end{matrix}] + [\begin{matrix} x_{i} (t) \\ y_{i} (t) \\ φ_{i} (t) \end{matrix}]$ (1)

Where x_i = [x_i (t), y_i (t), φ_i (t)] ^T is the state vector of the UAV, (xi (t), yi (t)) denotes the position of the unmanned aerial vehicle i, i (t) denotes the direction angle of the unmanned aerial vehicle i, i (t) -π, π], the north direction is zero, the counterclockwise direction is positive, u_i = [v_i (t), ω_i (t)] ^T is the control vector input of the unmanned vehicle i, vi (t) represents the velocity, and ωi (t) represents the angular velocity. Supposing the sampling time is ΔT, the corresponding discrete values are denoted as xi (k), yi (k), vi (k) and ωi (k) at the kth sampling time[k, k+1], all control inputs are constant, they are ${\dot{v}}_{i} (k) = 0$ and ${\dot{ω}}_{i} (t) = 0$ , the UAV’s discrete equation of motion can be written as follows: $x_{i} (k + 1) = x_{i} (k) + \frac{v_{i} (k) (sin φ_{i} (k + 1) - sin φ_{i} (k))}{ω_{i} (k)}$ (2) $y_{i} (k + 1) = y_{i} (k) + \frac{v_{i} (k) (\cos φ_{i} (k + 1) - cos φ_{i} (k))}{ω_{i} (k)}$ (3) $φ_{i} (k + 1) = φ_{i} (k) + ω_{i} (k) Δ T$ (4)

The above equation is written as a discrete state space model is as follows: $x_{i} (k + 1) = A_{ik} x_{i} (k) + B_{ik} x_{i} (k)$ (5) $y_{i} (k + 1) = C_{ik} x_{i} (k + 1)$ (6)

In the equation, yi (k + 1) represents the UAV output vector, and Aik, Bik, Cik satisfy the following three equations. $A_{ik} = C_{ik} = [\begin{matrix} 1 0 0 \\ 0 1 0 \\ 0 0 1 \end{matrix}]$ (7) $B_{ik} = [\begin{matrix} \frac{v_{i} (k) (sin φ_{i} (k + 1) - sin φ_{i} (k))}{ω_{i} (k)} 0 \\ \frac{v_{i} (k) (\cos φ_{i} (k + 1) - cos φ_{i} (k))}{ω_{i} (k)} 0 \\ 0 Δ T \end{matrix}]$ (8)

3.3 Rolling optimization process

At each sampling time, MPC obtains the optimal control sequence of the system at present by solving a finite time domain optimization problem, so that the system can realize online closed-loop control in the entire control time domain. Unmanned vehicle synergies to avoid collision DMPC controller rolling optimization work, the local state of the sensor from the machine and sent to the MPC controller, whether the need for collision avoidance judgment by the collision management unit collision management and sequencing module If there is a collision conflict, the MPC controller receives the ID number of the collision-avoidance vehicle from the collision management and sequencing module and reads the predicted trajectory of the unmanned vehicle according to this, and then from the coordinated collision avoidance control constraint The generating module receives the control constraint and the distance constraint, and obtains the prediction state with the control parameter through the prediction model. The optimization objective function is pre-set, so as to obtain a step of rolling online optimization problem. After solving the one-step optimization problem by a certain algorithm, the result is output to the UAV motion control unit.

(1) Optimization index. Optimization index taken as ability - the optimal combination of time, UAV collision avoidance optimal control index can be described by the following: $J_{ik} = {∥ Y_{i} (k) - Y_{ri} (k) ∥}_{Q}^{2} + {∥ Δ U_{i} (k) ∥}_{R}^{2}$ (9)

In the type: $Y_{i} (k) = [\begin{matrix} y_{i} (k + 1 / k) \\ y_{i} (k + 2 / k) \\ ⋮ \\ y_{i} (k + N / k) \end{matrix}]$ (10) $Y_{ri} (k) = [\begin{matrix} y_{ri} (k + 1 / k) \\ y_{ri} (k + 2 / k) \\ ⋮ \\ y_{ri} (k + N / k) \end{matrix}]$ (11) $Δ U_{i} (k) = [\begin{matrix} Δ u_{i} (k + 1 / k) \\ Δ u_{i} (k + 2 / k) \\ ⋮ \\ Δ u_{i} (k + N / k) \end{matrix}]$ (12)

yri (k) is the reference trajectory. The purpose of this algorithm is to avoid the process of drastic changes in input and output, requiring the current output yi (k) to reach the UAV target state yTi (k) along a desired, gentle curve. Reference trajectories are widely used first-order index changes. $y_{r i} (k + i / k) = y_{r i}^{'} (k) - e^{- Δ T / T_{r}} (y_{T i} (k) - y_{i} (k))$ (13)

(2) Constraints. a) UAV performance constraints. $| {\dot{v}}_{i} (k) | \leq {\dot{v}}_{max}^{i}$ (14) $| {\dot{ω}}_{i} (k) | \leq {\dot{ω}}_{max}^{i}$ (15) $| v_{i} (k) | \leq v_{max}^{i}$ (16) $| ω_{i} (k) | \leq ω_{max}^{i}$ (17)

Where ${\dot{v}}_{max}^{i}$ , ${\dot{ω}}_{max}^{i}$ , $v_{max}^{i}$ , $ω_{max}^{i}$ respective the unmanned aerial vehicle i acceleration, angular acceleration, velocity, angular velocity maximum.

b) Collision avoidance control constraints. ${\dot{v}}_{min ca}^{i} (k) \leq {\dot{v}}_{i} (k) \leq {\dot{v}}_{max ca}^{i} (k)$ (18) ${\dot{ω}}_{min ca}^{i} (k) \leq {\dot{ω}}_{i} (k) \leq {\dot{ω}}_{max ca}^{i} (k)$ (19) $v_{min ca}^{i} (k) \leq v_{i} (k) \leq v_{max ca}^{i} (k)$ (20) $ω_{min ca}^{i} (k) \leq ω_{i} (k) \leq ω_{max ca}^{i} (k)$ (21)

Where ${\dot{v}}_{min ca}^{i} (k)$ , ${\dot{v}}_{max ca}^{i} (k)$ , ${\dot{ω}}_{min ca}^{i} (k)$ , ${\dot{ω}}_{max ca}^{i} (k)$ , $v_{min ca}^{i} (k)$ , $v_{max ca}^{i} (k)$ , $ω_{min ca}^{i} (k)$ and $ω_{max ca}^{i} (k)$ are the extreme values of acceleration, angular acceleration, velocity, and angular velocity for unmanned aerial vehicle, respectively, as determined by the cooperative collision avoidance rules.

c) Unmanned aerial vehicle collision avoidance distance constraints Each UAV periodically sends out its MPC-calculated prediction information. The UAVs located within a certain range of their communication distance can receive their information and process it. Definition ${\tilde{X}}_{k}^{i} (t)$ is None At the moment t of the k-th step of passenger car i, t∈ (tk, tk+N * ΔT), that is ${\tilde{X}}_{k}^{i} (t) = {\tilde{x}}_{k}^{i} (t), {\tilde{y}}_{k}^{i} (t)$ (22)

Defining ${\tilde{X}}_{k}^{- i} (t)$ as k, the predicted trajectory information sent by unmanned aerial vehicle j which is received by unmanned aerial vehicle i, there is distance constraint in the unmanned aerial vehicle j own position at time t: $∥ {\tilde{X}}_{k}^{i} (t_{k} + n^{*} Δ T) - {\tilde{X}}_{k}^{- i} (t_{k} + n^{*} Δ T) ∥ \geq d_{s}$ (23)

3.4 Collision avoidance strategy

For each unmanned vehicle i∈V unmanned vehicle, the conflicts that need to be dealt with in the current moment are determined (unmanned vehicle p, $t_{col}^{i, p} (t_{k}) \in C^{i} (t_{k})$ , and unmanned vehicle i and unmanned vehicle p leader-follower relationship. In order to ensure conflict between two unmanned vehicles to deal with conflicts in a distributed manner and to ensure the consistency of the actions, the design of the rules based on the perspective of angle control strategy is shown in the following formula. $Δ θ_{m} \leq 0, Δ θ_{s} < 0 0 \leq η \leq π$ (24) $Δ θ_{m} > 0, Δ θ_{s} > 0 0 < η \leq 2 π$ (25)

Where θm, θs, Δθm and Δθs are the heading and heading control increments of the leader node and the heading angle and heading angle increment of the follower node respectively, and θm ∈ [π) and θs ∈ 0 r2π) r hand rule to determine the heading direction is positive. η=θm-θs rwhich is the difference between the heading angles of leader and follower. Cooperative heading angle control rules diagram shown in Fig. 1.

Fig.1

Angle control rules.

4 Result analysis and discussion

4.1 Simulation analysis

In this paper, the MATLAB optimization kit is used to solve the MPC rolling optimization process. If there is a collision conflict at any sampling time, the optimization problem is a nonlinear programming problem, which is solved by fmincon. If there is no collision, the step is optimized to the standard quadratic programming problem, which is solved by MATLAB optimization tool quadprog. In order to verify the effectiveness of the distributed cooperative collision avoidance method designed in this paper, two unmanned aerial vehicle (UAV) and four unmanned aerial vehicle (UAV) Collision avoidance process simulation, assuming the entire process of unmanned vehicle speed remains unchanged. The basic parameters are set as follows

ΔT = 1 s, N = 20, Nc = 10, dif = 5000 m, ds = 500 m $Q (n) = [\begin{matrix} 100 0 0 \\ 0 100 0 \\ 0 0 100 \end{matrix}]$ (26) $R (n) = [\begin{matrix} 1 0 \\ 0 1 \end{matrix}], n = 1, 2, \dots \dots, N$ (27)

To simplify the calculation, it is assumed that only the first term in the MPC predictive control sequence is not 0, that is, the angular velocity input sequence in the MPC predictive control sequence is (ω1,0,&, 0). Assuming that the UAV acquires its own state information is completely accurate, that is, the state acquired by the unmanned vehicle at the current moment in the simulation is equal to the current state of the MPC output by the model calculation at the previous moment.

(1) 2 unmanned vehicles coordinated avoidance. UAV initial information, end information, performance parameters set as shown in Table 1. Simulation program to run the basic computer configuration: Intel Corei33.1 GHz, 3G memory. Set the number of simulation steps to 100 steps, MPC single cycle running time of 0.21 s maximum, the average running time of 0.11 s, to meet the real-time requirements ΔT = 1 s conditions. The rule is shown in the simulation results as shown in Fig. 2. 2 unmanned vehicles set the same performance parameters, the initial state, the target state and the other side of the unmanned vehicle opposite, from Fig. 2a, b can be seen that two unmanned vehicles during the entire simulation cycle changes in accordance with the direction angle Rules, the angle of change is exactly the same. For visualization, the directional angle shown in Fig. 2b) is not constrained to be within the [0,2π) range. The distance between 2 unmanned vehicles displayed in Fig. 2C is 2. The value of the minimum safety distance between the 2 driverless cars and the minimum safety distance is DS. It can be seen that the value is all above the longitudinal axis. At step 30, the minimum distance between the two unmanned vehicles is 501.72 m. At step 60, two unmanned vehicles arrive at the same time. The results show that the two unmanned vehicles through the design of this paper can effectively achieve distributed cooperative collision avoidance.

Fig.2

Unmanned vehicle collision avoidance simulation results.

Table 1

Unmanned vehicle parameter list (2 unmanned vehicles)

Serial number of unmanned vehicle	initial status/(m, m, rad)	Initial statud/(m, m, rad)	velocity/(m·s–1)	palstance/(rad·s–1)	angular acceleration/(rad·s–2)
1	(5000, 0, π)	(0, 0, —)	85	–0.1, 0.1]	[–0.1, 0.1]
2	(0, 0, 0)	(5000, 0, —)	85	[–0.2, 0.2]	[–0.1, 0.1]

(2) 4 unmanned multi-collision collision avoidance. 4 unmanned vehicles initial information, end information, parameter settings such as shown in Table 2. According to the initial parameters set, without collision avoidance processing, there will be (unmanned aerial vehicle 2, unmanned aerial vehicle 4,18 s), (unmanned aerial vehicle 1, unmanned aerial vehicle 2,26 s), unmanned aerial vehicle 1, Unmanned aerial vehicle 3,26 s), (unmanned aerial vehicle 2, unmanned aerial vehicle 3,28 s) 4 sets of collision collisions, the second collision occurs simultaneously with the third collision, and only 4 seconds apart from the second collision. Using the collision avoidance rule, the simulation results are shown in Fig. 3.

Fig.3

Unmanned vehicle collision avoidance simulation results.

Table 2

Unmanned vehicle parameter list (4 unmanned vehicles)

Serial number of unmanned vehicle	initial status/(m, m, rad)	Initial status/(m, m, rad)	velocity/(m·s–1)	palstance/(rad·s–1)	angular acceleration/(rad·s–2)
1	(5000,0, π)	(0,5000,—)	90	[–0.2, 0.2]	[–0.1, 0.1]
2	(0,0, π/4)	(5000,5000,—)	90	[–0.2, 0.2]	[–0.1, 0.1]
3	(5000, 2500,π)	(0,3000,—)	60	[–0.2, 0.2]	[–0.1, 0.1]
4	(0, 1500,0)	(0,3000,—)	70	[–0.2, 0.2]	[–0.1, 0.1]

In this simulation, we still use the rule of directional angle change to conduct distributed autonomous cooperative collision avoidance, and the unmanned vehicle speed remains the same. It can be seen from Fig. 3 that four unmanned vehicles can effectively perform distributed cooperative collision avoidance with the collision avoidance solution designed in this paper, especially for the occurrence of multiple sets of conflicts occurring at the same time or at minimum intervals Effectively solve and solve the possible chain reaction caused by distributed collision avoidance control of unmanned vehicles when multiple conflicts occur simultaneously, and the distance between four unmanned vehicles is always greater than the safety distance. It can be seen from Fig. 3a) that the trajectories of the 4 unmanned vehicles after the collision avoidance control are smaller than the ones without the collision avoidance. It can be seen from Fig. 3c) that after the distributed collision avoidance control, the change of the state of the unmanned vehicle to solve the previous conflict leads to the new conflict or the original subsequent conflict automatically eliminated, and the finally resolved conflict The sequence is not exactly the same as the originally set conflict sequence.

4.2 Scheme Comparison

For the four UAV initial and target states set in this paper, under the same simulation environment, this paper adopts the scheme of “Low-priority unmanned vehicles to avoid high-priority unmanned vehicles As a moving obstacle to avoid “program to compare. Contrast analysis will only be unmanned plant collision avoidance strategy was replaced, the other modules are exactly the same. For the sake of simplification, the following article calls the collision avoidance strategy of this paper as scheme one, and the scheme of “low priority unmanned vehicle regards high priority unmanned vehicle as a moving obstacle to circumvent” as the second scheme. Assuming 4 unmanned vehicles according to the urgency of the mission, the order of priority from high to low is unmanned vehicle 1, unmanned aerial vehicle 2, unmanned aerial vehicle 3, and unmanned aerial vehicle 4. Because fmincon function is used in MATLAB optimization toolkit, a random function is used to initialize the initial value so that the solution has a certain randomness. Therefore, both schemes are run for 20 times, and the mean and mean square deviation of arrival time of 4 unmanned vehicles, The total control volume mean and standard deviation of four indicators were compared. Since the unmanned vehicle speed remains unchanged in both scenarios, the total amount of control is defined as shown in the following equation.

$\begin{matrix} C_{total}^{i} = \sum_{k = 1}^{Nstep} {| ω_{i} (t_{k}) - ω_{i} (t_{k - 1}) |}^{2} i \\ = 1, 2, 3, \dots \dots, N_{UAV} \end{matrix}$ (28)

Using the solution in this paper, all the feasible results are simulated within the set 150 steps. The statistical results are shown in Table 3. Where EX (Tr), SX (Tr), EX (C), SX (C), Ref (Tr) and Ref (C) denote the mean of arrival time, mean square deviation of arrival time, The variance, arrival time reference, total control reference, arrival time reference, and total control reference are the time of arrival without collision avoidance and the total control. When the second scheme is used, in 20 simulations, the program is terminated in 150 steps in 7 times, and some unmanned vehicles have not reached the target state. The operating statistics of the remaining 13 feasible solutions are shown in Table 4.

Table 3

Scenario 1 simulation results

Serial number of unmanned vehicle	EX(Tr)	SX(Tr)	EX(C)	SX(C)	Ref(Tr)
1	79.8	0.45	0.48	0.00	79
2	80.8	0.45	0.45	0.00	79
3	87.6	2.07	0.64	0.21	84
4	91.6	1.95	0.35	0.03	77

Table 4

Scenario 2 simulation results

Serial number of unmanned vehicle	EX(Tr)	SX(Tr)	EX(C)	SX(C)	Ref(Tr)	Ref(C)
1	79	0	0	0	79	0
2	83.2	6.06	0.72	0.16	79	0
3	96.4	7.64	0.47	0.12	84	0.02
4	90.8	11.65	0.90	0.30	77	0.03

By contrast, we can draw the following conclusions: a) In the mean time of arrival, the unmanned vehicle 2, unmanned vehicle 3, unmanned vehicle 4 in time, One due to collision avoidance motion caused by smaller trajectory deviation. And the mean square deviation of arrival time is small, the stability of solution is higher than that of scheme II. In the scheme 2, the unmanned aerial vehicle 1 does not perform the collision avoidance control because the fixed priority and the high priority are not used for collision avoidance. b) Indicators on the amount of control, the two programs in the average control over the average no significant advantages and disadvantages, the mean and were 1.915, 2.085. The average variance of the total control volume of scheme one is less than that of scheme two in total, indicating that the stability of the solution in multiple simulations is higher than that of scheme two.

5 Conclusion

As car ownership increases, the incidence of traffic jams and traffic accidents is rising. As an important solution to this problem, the research on driverless cars has become increasingly urgent. This paper studied and analyzed the active obstacle avoidance algorithm based on the model predictive control, designed and proposed a collaborative collision avoidance trajectory planning scheme, and transformed the collision avoidance process into a rolling online optimization problem. Aiming at the problem of multi-collision conflict management, a distributed collision avoidance management unit was designed. The interactive graph update mechanism was used to manage and sort the conflicts. Aiming at the consistency of motion avoidance, a coordinated collision avoidance control strategy based on the change rule of directional angle was designed. The simulation results show that the proposed scheme can effectively solve the collision avoidance problem in unmanned workshop.

Footnotes

Acknowledgments

Supported by China Automobile Industry Innovation and Development Joint Fund,Four-Wheel Drive Electric Vehicle Chassis Dynamic Coordinated Control and Vehicle Energy Optimization Management (NO. U1664257).

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