Multi-Car Convex Feasible Set Algorithm in Trajectory Planning

2020 ◽  
Author(s):  
Jing Huang ◽  
Changliu Liu
Keyword(s):  
Convex Optimization ◽  
Quadratic Programming ◽  
Real Time ◽  
Trajectory Planning ◽  
Autonomous Driving ◽  
Curse Of Dimensionality ◽  
Planning Problem ◽  
Feasible Set ◽  
Planning Algorithm ◽  
Vehicle Trajectory

Abstract Trajectory planning is an essential module for autonomous driving. To deal with multi-vehicle interactions, existing methods follow the prediction-then-plan approaches which first predict the trajectories of others then plan the trajectory for the ego vehicle given the predictions. However, since the true trajectories of others may deviate from the predictions, frequent re-planning for the ego vehicle is needed, which may cause many issues such as instability or deadlock. These issues can be overcome if all vehicles can form a consensus by solving the same multi-vehicle trajectory planning problem. Then the major challenge is how to efficiently solve the multi-vehicle trajectory planning problem in real time under the curse of dimensionality. We introduce a novel planner for multi-vehicle trajectory planning based on the convex feasible set (CFS) algorithm. The planning problem is formulated as a non-convex optimization. A novel convexification method to obtain the maximal convex feasible set is proposed, which transforms the problem into a quadratic programming. Simulations in multiple typical on-road driving situations are conducted to demonstrate the effectiveness of the proposed planning algorithm in terms of completeness and optimality.

Optimal Trajectory Generation for Intelligent Vehicles in Complex Traffic Based on Iteration Convex Optimization

2021 ◽  
pp. 2159040
Author(s):  
Xiaoyu Zhang ◽  
Aihua Li
Keyword(s):  
Convex Optimization ◽  
Quadratic Programming ◽  
Trajectory Planning ◽  
Three Dimensional ◽  
Intelligent Vehicles ◽  
Feasible Region ◽  
Planning Problem ◽  
Time Varying ◽  
The Road ◽  
On The Road

Intelligent vehicles face considerable challenges in the complex traffic environment since they need to deal with various constraints and elements. This dissertation puts forward a novel trajectory planning framework for intelligent vehicles to generate safe and optimal driving trajectories. First, we design a spatiotemporal occupancy framework to deal with all kinds of elements in the complex driving environment based on the Frenét frame. This framework unifies various constraints on the road in the three-dimensional spatiotemporal representation and clearly describes the collision-free configuration space. Then we use the convex approximation method to construct a time-varying convex feasible region based on the above accurate temporal and spatial description. We formulate the trajectory planning problem as a standard quadratic programming formulation with collision-free and dynamics constraints. Finally, we apply the iterative convex optimization algorithm to solve the quadratic programming problem in the time-varying convex feasible region. Moreover, we design several typical experimental scenarios and have verified that the proposed method has good effectiveness and real-time.

scholarly journals Real - Time Trajectory and Velocity Planning for Autonomous Vehicles

2021 ◽  
Vol 10 (5) ◽  
pp. 439-448
Author(s):  
Hrishikesh Dey ◽  
Rithika Ranadive ◽  
Abhishek Chaudhari
Keyword(s):  
Path Planning ◽  
Velocity Profile ◽  
Real Time ◽  
Autonomous Vehicle ◽  
Optimal Path ◽  
Autonomous Driving ◽  
Navigation Algorithm ◽  
Velocity Planning ◽  
Planning Algorithm ◽  
Path Planner

Path planning algorithm integrated with a velocity profile generation-based navigation system is one of the most important aspects of an autonomous driving system. In this paper, a real-time path planning solution to obtain a feasible and collision-free trajectory is proposed for navigating an autonomous car on a virtual highway. This is achieved by designing the navigation algorithm to incorporate a path planner for finding the optimal path, and a velocity planning algorithm for ensuring a safe and comfortable motion along the obtained path. The navigation algorithm was validated on the Unity 3D Highway-Simulated Environment for practical driving while maintaining velocity and acceleration constraints. The autonomous vehicle drives at the maximum specified velocity until interrupted by vehicular traffic, whereas then, the path planner, based on the various constraints provided by the simulator using µWebSockets, decides to either decelerate the vehicle or shift to a more secure lane. Subsequently, a splinebased trajectory generation for this path results in continuous and smooth trajectories. The velocity planner employs an analytical method based on trapezoidal velocity profile to generate velocities for the vehicle traveling along the precomputed path. To provide smooth control, an s-like trapezoidal profile is considered that uses a cubic spline for generating velocities for the ramp-up and ramp-down portions of the curve. The acceleration and velocity constraints, which are derived from road limitations and physical systems, are explicitly considered. Depending upon these constraints and higher module requirements (e.g., maintaining velocity, and stopping), an appropriate segment of the velocity profile is deployed. The motion profiles for all the use-cases are generated and verified graphically.

A Comparison of Trajectory Planning and Control Frameworks for Cooperative Autonomous Driving

2021 ◽  
Vol 143 (7) ◽  
Author(s):  
Icaro Bezerra Viana ◽  
Husain Kanchwala ◽  
Kenan Ahiska ◽  
Nabil Aouf
Keyword(s):  
Trajectory Planning ◽  
Cooperative Behavior ◽  
Autonomous Driving ◽  
General Idea ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Change Scenario ◽  
Planning Problem ◽  
Lane Change ◽  
Double Lane Change

Abstract This work considers the cooperative trajectory-planning problem along a double lane change scenario for autonomous driving. In this paper, we develop two frameworks to solve this problem based on distributed model predictive control (MPC). The first approach solves a single nonlinear MPC problem. The general idea is to introduce a collision cost function in the optimization problem at the planning task to achieve a smooth and bounded collision function, and thus to prevent the need to implement tight hard constraints. The second method uses a hierarchical scheme with two main units: a trajectory-planning layer based on mixed-integer quadratic program (MIQP) computes an on-line collision-free trajectory using simplified motion dynamics, and a tracking controller unit to follow the trajectory from the higher level using the nonlinear vehicle model. Connected and automated vehicles (CAVs) sharing their planned trajectories lay the foundation of the cooperative behavior. In the tests and evaluation of the proposed methodologies, matlab-carsim cosimulation is utilized. carsim provides the high-fidelity model for the multibody vehicle dynamics. matlab-carsim conjoint simulation experiments compare both approaches for a cooperative double lane change maneuver of two vehicles moving along a one-way three-lane road with obstacles.

Cooperative Trajectory Planning for Multi-UCAV Performing Air-to-Ground Target Attack Missions

2013 ◽  
Vol 718-720 ◽  
pp. 1329-1334 ◽  
Author(s):  
Xue Qiang Gu ◽  
Yu Zhang ◽  
Shao Fei Chen ◽  
Jing Chen
Keyword(s):  
Trajectory Planning ◽  
Differential Flatness ◽  
Planning Problem ◽  
Temporal Constraints ◽  
Differential Flatness Theory ◽  
Spline Curves ◽  
Ground Target ◽  
Planning Algorithm ◽  
Virtual Time ◽  
Unmanned Combat Aerial Vehicles

The problem of planning flight trajectories is studied for multiple unmanned combat aerial vehicles (UCAVs) performing a cooperated air-to-ground target attack (CA/GTA) mission. Several constraints including individual and cooperative constraints are modeled, and an objective function is constructed. Then, the cooperative trajectory planning problem is formulated as a cooperative trajectory optimal control problem (CTP-OCP). Moreover, in order to handle the temporal constraints, a notion of the virtual time based strategy is introduced. Afterwards, a planning algorithm based on the differential flatness theory and B-spline curves is developed to solve the CTP-OCP. Finally, the proposed approach is demonstrated using a typical CA/GTA mission scenario, and the simulation results show that the proposed approach is feasible and effective.

Mixed Integer Linear Programming for UAV Trajectory Planning Problem

2014 ◽  
Vol 541-542 ◽  
pp. 1473-1477 ◽  
Author(s):  
Lei Zhang ◽  
Zhou Zhou ◽  
Fu Ming Zhang
Keyword(s):  
Real Time ◽  
Predictive Control ◽  
Trajectory Planning ◽  
Arrival Time ◽  
Linear Constraints ◽  
Mixed Integer ◽  
Planning Problem ◽  
Convex Constraints ◽  
3D Environments ◽  
On Line

This paper describes a method for vehicles flying Trajectory Planning Problem in 3D environments. These requirements lead to non-convex constraints and difficult optimizations. It is shown that this problem can be rewritten as a linear program with mixed integer linear constraints that account for the collision avoidance used in model predictive control, running in real-time to incorporate feedback and compensate for uncertainty. An example is worked out in a real-time scheme, solved on-line to compensate for the effect of uncertainty as the maneuver progresses. In particular, we compare receding horizon control with arrival time approaches.

scholarly journals Path Planning for Highly Automated Driving on Embedded GPUs

2018 ◽  
Vol 8 (4) ◽  
pp. 35 ◽  
Author(s):  
Jörg Fickenscher ◽  
Sandra Schmidt ◽  
Frank Hannig ◽  
Mohamed Bouzouraa ◽  
Jürgen Teich
Keyword(s):  
Path Planning ◽  
Real Time ◽  
Autonomous Driving ◽  
Automated Driving ◽  
Computing Power ◽  
Planning Algorithm ◽  
Time Requirements ◽  
Evaluation Platform ◽  
Path Planning Algorithm ◽  
Highly Automated Driving

The sector of autonomous driving gains more and more importance for the car makers. A key enabler of such systems is the planning of the path the vehicle should take, but it can be very computationally burdensome finding a good one. Here, new architectures in ECU are required, such as GPU, because standard processors struggle to provide enough computing power. In this work, we present a novel parallelization of a path planning algorithm. We show how many paths can be reasonably planned under real-time requirements and how they can be rated. As an evaluation platform, an Nvidia Jetson board equipped with a Tegra K1 SoC was used, whose GPU is also employed in the zFAS ECU of the AUDI AG.

Real-Time Cooperative Trajectory Planning Using Differential Flatness Approach and B-Splines

2013 ◽  
Vol 333-335 ◽  
pp. 1338-1343 ◽  
Author(s):  
Xue Qiang Gu ◽  
Yu Zhang ◽  
Jing Chen ◽  
Lin Cheng Shen
Keyword(s):  
Optimal Control ◽  
Real Time ◽  
Trajectory Planning ◽  
Differential Flatness ◽  
Planning Problem ◽  
Receding Horizon ◽  
B Splines ◽  
Battlefield Environment ◽  
Planning Space ◽  
Spatial Trajectories

This paper proposed a cooperative receding horizon optimal control framework, based on differential flatness and B-splines, which was used to solve the real-time cooperative trajectory planning for multi-UCAV performing cooperative air-to-ground target attack missions. The planning problem was formulated as a cooperative receding horizon optimal control problem (CRHC-OCP), and then the differential flatness and B-splines were introduced to lower the dimension of the planning space and parameterize the spatial trajectories. Moreover, for the dynamic and uncertainty of the battlefield environment, the cooperative receding horizon control was introduced. Finally, the proposed approach is demonstrated, and the results show that this approach is feasible and effective.

scholarly journals Generic Trajectory Planning Algorithm for Urban Autonomous Driving

2021 ◽  
Author(s):  
Thibaud Duhautbout ◽  
Reine Talj ◽  
Veronique Cherfaoui ◽  
Francois Aioun ◽  
Franck Guillemard
Keyword(s):  
Trajectory Planning ◽  
Autonomous Driving ◽  
Planning Algorithm

scholarly journals Contact-Rich Trajectory Generation in Confined Environments Using Iterative Convex Optimization

2020 ◽  
Author(s):  
Wei-Ye Zhao ◽  
Suqin He ◽  
Chengtao Wen ◽  
Changliu Liu
Keyword(s):  
Convex Optimization ◽  
Motion Planning ◽  
Real Time ◽  
Trajectory Generation ◽  
Robot Kinematics ◽  
Planning Problem ◽  
Robot Arm ◽  
Task Constraints ◽  
Robot Arms ◽  
Highly Nonlinear

Abstract Applying intelligent robot arms in dynamic uncertain environments (i.e., flexible production lines) remains challenging, which requires efficient algorithms for real time trajectory generation. The motion planning problem for robot trajectory generation is highly nonlinear and nonconvex, which usually comes with collision avoidance constraints, robot kinematics and dynamics constraints, and task constraints (e.g., following a Cartesian trajectory defined on a surface and maintain the contact). The nonlinear and nonconvex planning problem is computationally expensive to solve, which limits the application of robot arms in the real world. In this paper, for redundant robot arm planning problems with complex constraints, we present a motion planning method using iterative convex optimization that can efficiently handle the constraints and generate optimal trajectories in real time. The proposed planner guarantees the satisfaction of the contact-rich task constraints and avoids collision in confined environments. Extensive experiments on trajectory generation for weld grinding are performed to demonstrate the effectiveness of the proposed method and its applicability in advanced robotic manufacturing.

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