Race driver model: trajectory planning

The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this speed profile fixed, the algorithm updates the vehicle’s path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs well when tested on the Thunderhill Raceway course in Willows, CA. The lap time reaches a minimum value after only three iterations, with each iteration over the full 5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting vehicle path and speed profile match very well with a nonlinear gradient descent solution and a path driven by a professional racecar driver, indicating that the proposed method is a viable option for online trajectory planning in the near future.

In this article, we focus on safe and effective completion of a rendezvous and docking task by looking at planning approaches and control with fuel-optimal rendezvous for a target spacecraft running on a near-circular reference orbit. A variety of existent practical path constraints are considered, including the constraints of field of view, impulses, and passive safety. A rendezvous approach is calculated by using a hybrid genetic algorithm with those constraints. Furthermore, a control method of trajectory tracking is adopted to overcome the external disturbances. Based on Clohessy–Wiltshire equations, we first construct the mathematical model of optimal planning approaches of multiple impulses with path constraints. Second, we introduce the principle of hybrid genetic algorithm with both stronger global searching ability and local searching ability. We additionally explain the application of this algorithm in the problem of trajectory planning. Then, we give three-impulse simulation examples to acquire an optimal rendezvous trajectory with the path constraints presented in this article. The effectiveness and applicability of the tracking control method are verified with the optimal trajectory above as control objective through the numerical simulation.

This paper is focused on the cooperative trajectory planning problem for multiple car-like robots in a cluttered and unstructured environment narrowed by static obstacles. The concerned multi-vehicle trajectory planning (MVTP) problem is challenging because i) the scenario is nonconvex and tiny; ii) the vehicle kinematics is nonconvex; and iii) a feasible homotopy class is unavailable a priori. We propose a two-stage MVTP method: Stage 1 identifies a feasible homotopy class, and Stage 2 quickly finds a local optimum based on the identified homotopy class. Numerical optimal control, adaptive scaling, grouping, and trust region construction strategies are integrated into the proposed planner. Our planner is extensively compared in 100 benchmark cases with the state-of-the-art MVTP methods such as incremental sequential convex programming, numerical optimal control, conflict-based search, priority-based trajectory optimizer, and optimal reciprocal collision avoidance. The simulation results demonstrate our method's superiority in runtime and optimality. Experiments with three car-like robots demonstrate the efficiency of our proposed planner. Source codes are in https://github.com/libai1943/MVTP_benchmark.

The problem of trajectory planning is one of the important tasks of autonomous mobile robots (AMR). For that, in this paper, a trajectory planning algorithm is developed to generate a smooth trajectory for AMR in a static environment. The generated trajectory links a starting point with an end point while avoiding static obstacles. The trajectory curve is parameterized with the B-spline interpolation due to its smoothness properties and to reduce the number of points needed to define. Therefore, to find the optimal B-spline parameters, the trajectory planning problem has turned into an optimization problem. Improved Grey Wolf Optimizer (I-GWO) was selected as optimization algorithm because of its excellent optimization performance and global search capability. Different I-GWO settings were tested and the best selected setting was compared with other optimization algorithms. The results show that the selected optimization algorithm is more efficient and accurate.

<div class="section abstract"><div class="htmlview paragraph">Lane Centering Control System (LCCS) is a lateral Advanced Driving Assistance System (ADAS) with low acceptance. One of the main reasons is that the centering trajectory can’t satisfy different drivers, which is more obvious in the curve condition. So LCCS adaptive to different drivers needs to be designed. The trajectory planning module is an important part for LCCS. It generates trajectory according to the road information for the vehicle control module to track. This paper uses road information obtained from the scenario established in Prescan, and the trajectory planning method proposed can generate trajectories for different drivers in the curve condition. To achieve the goal, this paper proposes a trajectory planning method which contains lateral path planning and longitudinal speed planning. Firstly, the overall strategy of “road equidistant segments division” is used to describe the road information. Secondly, the path planning method establishes objective functions for four typical driving modes respectively, including shortest length, minimum curvature, centering driving, and minimum heading angle deviation, which solved by quadratic programming. Then the mixed mode path is obtained by weighting four different paths. Thirdly, a speed planning method is proposed. The speed profile is described by the natural cubic spline and it’s based on the generated path which considers different constraints of longitudinal and lateral acceleration of different drivers and the trajectory is generated by coupling speed profile with the path. Finally, the co-simulation of Matlab/Simulink and Prescan is carried out in different scenarios, and the simulation result is analyzed. The simulation result shows that the trajectory planning method proposed in this paper can generate trajectories for different drivers under the constraints of the tire dynamics, and the feasibility of the algorithm is verified.</div></div>

In the convex optimization problem for entry trajectory planning, the middle variables as new controls are defined to reduce the difficulty of convexification of original problem. Because of some reasons, the discontinuous or non-smooth of profiles of commands appear when solving commands using middle variables. For handling the phenomenon, a solution method of guidance commands via low-pass filter is proposed in this paper. Firstly, a discretized convex trajectory planning problem is formulated. Secondly, the solution errors of commands are defined. On the discretization points with high error, the proposed method is performed to smooth the abnormal commands by commands updating equations. On the other discretization points with low error, the method is not necessary. Finally, the method is inserted into a sequential iteration algorithm to solve the original non-convex entry trajectory planning problem. In numerical simulation, the effectiveness of the proposed method is verified, and the influence of filter coefficients on convergence and accuracy is discussed.KeywordsGuidance commandsLow-pass filterConvex trajectory planning

Unmanned Aerial Vehicles (UAVs), in multi-UAV collaborative search systems, need to realize adaptive autonomous trajectory planning based on their own state and surrounding environmental conditions. To allow for a fast trajectory planning of multiple UAVs from the current state to the target state, this paper proposes a trajectory planning method for multi-UAV collaborative search tasks based on genetic algorithm (GA). And using genetic algorithm, the UAV's trajectory can be optimized online based on the current mission. Through the analysis of the tasks of the multi-UAV collaborative decision-making part and the autonomous trajectory planning part, the genetic algorithm is used to model and optimize the trajectory planning problem to obtain a feasible and efficient optimal search trajectory from the current state to the decision-making target state. Finally, through specific simulation experiments, the optimal trajectory from the current state to the target state of the UAV i in the multi-UAV system is obtained, which verifies the effectiveness of the algorithm.

The problem of trajectory planning and obstacle avoidance in redundant robots is addressed in this paper. Four variants of Particle Swarm Optimization (PSO) and a Differential Evolution (DE) algorithm are proposed to solve this problem. Simulation experiments on a 5 degree-of-freedom (DOF) robot manipulator in an environment with static obstacles are conducted. The manipulator is required to move from a start position to a goal position with minimum error while avoiding collision with the obstacles in the workspace. The performance of the proposed algorithms is compared with the results reported in the literature and the comparative results are presented. It is observed that qPSO-C performs better in free space and PSO-C performs better in environment with obstacles in terms of minimizing error average convergence time. The performance of DE improves when the number of obstacles increases.

Purpose The purpose of this paper is to improve the positional accuracy, smoothness on motion and productivity of industrial robot through the proposed optimal joint trajectory planning method. Also a new improved algorithm, i.e. non-dominated sorting genetic algorithm-II (NSGA-II) with achievement scalarizing function (ASF) has been proposed to obtain better optimal results compared to previously used optimization methods. Design/methodology/approach The end effector positional errors can be reduced by limiting the uncertainties of dynamic parameter variations like torque rate of joints. The jerk induced in robot joints due to acceleration variations are need to be minimized which otherwise induces vibrations in the manipulator that causes deviation in the encoders. But these lead to a vast increase in total travel time which affects the cost function of trajectory planning. Therefore, these three objectives need to be minimized individually so that an optimal trajectory path can be achieved with minimum positional error. Findings The simulation results have been obtained by running the proposed hybrid NSGA-II with ASF in MATLAB R2017a software. The optimal time intervals have been used to calculate jerk, acceleration and torque values for consecutive points on the trajectory path. From the simulation and experimental results, it can be concluded that the optimization technique could be used effectively for the trajectory planning of six-axis industrial manipulator in the joint space on the basis of minimum time-jerk-torque rate criteria. Originality/value In this paper, a new approach based on hybrid multi-objective optimization technique by combining NSGA-II with ASF has been applied to find the minimal time-jerk- torque rate joint trajectory of a six-axis industrial robot for obtaining higher positional accuracy. The results obtained from the execution of algorithm have been validated through experimentation using Kawasaki RS06L industrial robot for a particular defined path.

As racing vehicles become more complex, optimising the interaction between subsystems becomes critical for racing performance. In this work, we incorporate two such subsystems into a vehicle model. We investigate the performance benefits of a four-wheel-drive vehicle with independent control over its in-hub motors and active control on the rear wing flap rotation. The performance is evaluated by solving minimum lap time optimal control problems (OCP) for various vehicle configurations. The OCP is transformed into a nonlinear programming problem through direct collocation and is solved by an interior point method. The four-wheel-drive configuration performs better than rear-wheel drive in terms of lap time, finishing the Barcelona circuit faster. The benefits come mainly from higher longitudinal accelerations. Active aerodynamic control improves performance regardless of the propulsion configuration, leading to another of lap time improvement on the Barcelona circuit. The optimal aerodynamic control strategy is different between propulsion configurations, particularly on corner exits. This model enables the exploration of optimal torque vectoring controls and their interaction with a vehicle's active aerodynamics. This is needed to guide the design of the increasingly complex racing vehicle controllers of the future.

The aim of this study was to develop trajectory planning that would allow an autonomous racing car to be driven as close as possible to what a driver would do, defining the most appropriate inputs for the current scenario. The search for the optimal trajectory in terms of lap time reduction involves the modeling of all the non-linearities of the vehicle dynamics with the disadvantage of being a time-consuming problem and not being able to be implemented in real-time. However, to improve the vehicle performances, the trajectory needs to be optimized online with the knowledge of the actual vehicle dynamics and path conditions. Therefore, this study involved the development of an architecture that allows an autonomous racing car to have an optimal online trajectory planning and path tracking ensuring professional driver performances. The real-time trajectory optimization can also ensure a possible future implementation in the urban area where obstacles and dynamic scenarios could be faced. It was chosen to implement a local trajectory planning based on the Model Predictive Control(MPC) logic and solved as Linear Programming (LP) by Sequential Convex Programming (SCP). The idea was to achieve a computational cost, 0.1 s, using a point mass vehicle model constrained by experimental definition and approximation of the car’s GG-V, and developing an optimum model-based path tracking to define the driver model that allows A car to follow the trajectory defined by the planner ensuring a signal input every 0.001 s. To validate the algorithm, two types of tests were carried out: a Matlab-Simulink, Vi-Grade co-simulation test, comparing the proposed algorithm with the performance of an offline motion planning, and a real-time simulator test, comparing the proposed algorithm with the performance of a professional driver. The results obtained showed that the computational cost of the optimization algorithm developed is below the limit of 0.1 s, and the architecture showed a reduction of the lap time of about 1 s compared to the offline optimizer and reproducibility of the performance obtained by the driver.

This study aims to develop prediction models of driver takeover time and crash risks during the automated driving takeover process. A driving simulator experiment was conducted to collect vehicle trajectory and driver behavior data. The random-parameter duration model was first built to model driver takeover time. Results indicated that young drivers, novice drivers, takeover request lead time, and traffic volume had varying impacts on takeover time due to the unobserved heterogeneity. Then, an explainable machine learning model was utilized to predict and explore various predictors’ impacts on takeover crashes. Validation results revealed that the developed model provided satisfactory accuracy in predicting crashes. SHAP was used to interpret the estimated results by examining contributory factors’ main effects and interactive effects on crash risks. Takeover crash risk is positively correlated with vehicle speed, takeover time, maximum lateral acceleration, traffic volume, and tasks of watching videos and playing games. Additionally, takeover request lead time and the maximum longitudinal deceleration were found to affect crash risks negatively. Research findings shed insights into modeling takeover time and predicting crash risks during the takeover process, and highlight the importance of considering the heterogeneity of drivers when designing automated driving systems (ADS) to improve driver takeover performance.

Modelling of road vehicles for calculation of traffic-induced ground vibration as a random process

This paper proposes an automated vehicle trajectory following system that uses four constrained wheel torques to regulate a vehicle on a reference trajectory. The constrained wheel torques can be achieved using the two-wheel drive and differential brakes. The proposed control algorithm is developed using the following steps. First, the sliding-mode control is used to find stability constraints for trajectory following when the vehicle system is subjected to modeling errors. Second, these stability constraints, along with other actuator constraints, are particularly tuned for the proposed control distribution method. The proposed control distribution method determines four longitudinal tire forces and minimizes actuator control efforts. Finally, these tire forces are converted to traction/braking wheel torques. The proposed method has the following advantages: 1) It achieves both robust trajectory following and optimal control efforts, 2) the optimal control effort is obtained analytically instead of from a numerical search, and 3) the robust performance of this vehicle control system can be theoretically verified. The proposed method is evaluated using numerical simulations on two front-drive vehicle models: a full-state vehicle model and a sedan model from the Carsim commercial software. The simulation results indicate that, in both cases, the proposed method can regulate the vehicle to finish a “double-lane change” when the vehicle is moving at an initial speed of 90 km/h. The maximum lateral acceleration is 6.56 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and the regulated position error is less than 6.9 cm.

&lt;div&gt;Single lane changing is one of the typical scenarios in vehicle driving. Planning an appropriate lane change trajectory is crucial in autonomous and semi-autonomous vehicle research. Existing polynomial trajectory planning mostly uses cubic or quintic polynomials, neglecting the lateral jerk constraints during lane changes. This study uses seventh-degree polynomials for lane change trajectory planning by considering the vehicle lateral jerk constraints. Simulation results show that the utilization of the seventh-degree method results in a 41% reduction in jerk compared to the fifth-degree polynomial. Furthermore, this study also proposes lane change trajectory schemes that can cater to different driving styles (e.g., safety, efficiency, comfort, and balanced performance). Depending on the driving style, the planned lane change trajectory ensures that the vehicle achieves optimal performance in one or more aspects during the lane change process. For example, with the trajectory that provides the best comprehensive performance under given constraints (initial speed of 20 m/s, lane width of 3.5 m, and a longitudinal distance of 50 m to the obstacle in front), the four-wheel steering model predictive control can effectively track the planned trajectory, with the maximum jerk value being 6.4 m/s&lt;sup&gt;3&lt;/sup&gt; and the longitudinal speed after lane change being approximately 12.6 m/s. Although this study assumes specific longitudinal displacement before and after the lane change, the methodology is applicable to other scenarios. For example, it can determine the shortest longitudinal displacement and the optimal lane change trajectory given predefined vehicle speeds and maximum lateral acceleration conditions. The lane change trajectories developed in this study can be directly applied to the system design of autonomous vehicles.&lt;/div&gt;