A Model for Autonomous Vehicle Obstacle Avoidance at High Speeds

Interdisciplinary Description of Complex Systems 22(3), 246-265, 2024 A MODEL FOR AUTONOMOUS VEHICLE OBSTACLE AVOIDANCE AT HIGH SPEEDS Dragan D. Stamenković* and Vladimir M. Popović University of Belgrade, Faculty of Mechanical Engineering Belgrade, Serbia DOI: 10.7906/indecs.22.3.2 Regular article Received: 21 May 2024. Accepted: 15 June 2024. ABSTRACT The systems that are currently installed in autonomous vehicles are not designed to avoid obstacles on the road by manoeuvring at the limits of the vehicle and the road surface – the goal of the research presented was to develop such system. For these purposes, a universal test track based on ISO 3888-1 and ISO 3888-2 standards was adopted, which can be used to represent any situation in which there is an obstacle on the road in front of the vehicle that needs to be avoided. An analysis of the curves for generating the paths through the test track was carried out, on the basis of which the Bézier curves were chosen. In addition to them, the results of simulations in Adams Car software were used to generate the paths, which can be considered equivalent to real-world trials with a professional driver behind the wheel. A control model was developed for longitudinal and transverse control of the vehicle based on PID controllers, with the selection of optimal parameters – the ones that define PID controllers, and the others that define other characteristics of the model. The model proved to be successful in guiding the vehicle through the test track at all speeds at which manoeuvres are possible. Bézier curves are shown to be a better choice at lower speeds, while paths based on Adams Car simulations are a better choice at higher speeds. KEY WORDS autonomous vehicle, lateral control, double lane change, moose test, vehicle dynamics CLASSIFICATION ACM: I.6.0 JEL: R49 *Corresponding author, : ; +381 63 656 254; *Kraljice Marije 16, 11120 Belgrade 35, Serbia A model for autonomous vehicle obstacle avoidance at high speeds INTRODUCTION The aim of the research presented in this article was to develop a model to control the autonomous vehicle in obstacle avoidance manoeuvres at high speeds. To the knowledge of the authors, there are no implemented systems that can guide the vehicle autonomously in a way to avoid the obstacle and safely return to the original lane at high speed at which stability of the vehicle can be impaired due to sharp manoeuvres. To achieve this, co-simulations were conducted according to the scheme shown in Figure 1. Adams Car was used to create the vehicle model that will be controlled by the Simulink model (acting as a driver). In this co-simulation, Simulink is sending control inputs (steering wheel, throttle, brake, clutch and transmission) to Adams Car, while Adams Car is returning the data on vehicle dynamic behaviour (position, speed, acceleration…) to Simulink, which uses it to adapt the control signals. Control signals Model feedback Simulink model Adams Car model Subsystem 2 Test bed Subsystem 1 Subsystem n Figure 1. Co-simulation scheme. To assess the stability and manoeuvrability of the vehicle, the tests described in the standards ISO 3888-1 (Double Lane Change Test) and ISO 3888-2 (“Moose” test) are used as a standard. These tests are carried out on the test track shown in Figure 2 and defined in Table 1. Test 1 defined in ISO 3888-1 standard is performed by passing through the defined test track, where the recommended speed for entering section 1 is 80 ± 3 km/h, and during the test the position of the throttle should be kept in a constant position, as long as it is that possible. x 1 2 3 4 5 Figure 2. Test track according to ISO 3888-1 and ISO 3888-2. 247 D.D. Stamenković and V.M. Popović When performing the “moose” test according to the ISO 3888-2 standard, section 1 is entered in the highest gear that provides at least 2 000 engine RPМ. Two meters after entering section 1, it is necessary to release the throttle and cross the rest of the test track with it being released. All simulations done for the purpose of this research, regardless of test track dimensions, were performed at a constant speed. Table 1. Test track dimensions according to ISO 3888-1 and ISO 3888-2 (b is vehicle width). Length, m Width, m Section ISO 3888-1 ISO 3888-2 ISO 3888-1 ISO 3888-2 1 15 12 2 30 13,5 3 25 11 4 25 12,5 5 30 12 1,1b + 0,25 x 1,2b + 0,25 b+1 1,3b + 0,25 min(1,3b + 0,25; 3) 3,5 1,1b + 1,25 For the purpose of the research, an important assumption was made – every situation in which a vehicle has to change its lane to avoid an obstacle can be represented by the universal test track shown in Figure 3. The universal test track is based on the test tracks defined by ISO 3888-1 and ISO 3888-2 standards, and its dimensions depend on the data obtained using the sensors and cameras on-board the vehicle, for example like in [1]. B2 Bp B1 L1 B1 B2 Bp L1 L1+L2 L3 L2+L3+L4 L4+L5 L2 L3 L4 L5 width of the ego vehicle’s lane width of the adjacent lane length of the obstacle projected distance between the ego vehicle and the vehicle in adjacent lane at the moment when ego vehicle enters the adjacent lane distance between the vehicle and the obstacle length of the obstacle free length in the adjacent lane free length in the original lane after the manoeuvre Figure 3. Universal test track. PATH DEFINITION Next step was to choose the curve for path generation. Figure 4 shows eight different paths created by drawing eight different curves through or next to the defined points on the test track prescribed by the ISO 3888-1 using MATLAB functions listed in Table 2. 248 A model for autonomous vehicle obstacle avoidance at high speeds Table 2. Curves used to construct path. Curve (with marks corresponding to Figure 3) a) b) c) d) e) f) g) h) MATLAB function Cubic spline Clamped cubic spline Piecewise cubic Hermite interpolating polynomial Cubic smoothing spline spline B-spline B-spline (smoothing) 3rd order Bézier curve Modified Akima spline spline Additional parameter(s) Starting and ending angles equal to zero Lowest curve radius at ISO 3888-1 test track [m] 70 100 pchip - 45 csaps Smoothness factor: 0,01 115 spmak Coefficients: 7; 7; 7 (three for 6th order) 90 spaps Tolerances: 0; 1; 1; 1; 1; 0 100 [2] - 70 makima - 60 Of the eight curves shown, six are splines, and the seventh is a combination of two Bézier curves, so it can also be considered a spline, although it was not created by applying De Castelju’s theorem. The points are chosen to be at the midpoint of the test track width at each point where the test track changes width, plus the start and the end of the test track. By moving the points towards the line that separates the two lanes (that is, towards the boundaries of the test track closer to this line), the curvature of the path would be reduced, which would allow the vehicle to pass at a higher speed, that is, reduce the pro (...truncated)