Game Theoretic Model Predictive Control for Autonomous Driving

This study presents two closely-related solutions to autonomous vehicle control problems in highway driving scenario using game theory and model predictive control. We first develop a game theoretic four-stage model predictive controller (GT4SMPC). The controller is responsible for both longitudinal and lateral movements of Subject Vehicle (SV) . It includes a Stackelberg game as a high level controller and a model predictive controller (MPC) as a low level one. Specifically, GT4SMPC constantly establishes and solves games corresponding to multiple gaps in front of multiple-candidate vehicles (GCV) when SV is interacting with them by signaling a lane change intention through turning light or by a small lateral movement. SV’s payoff is the negative of the MPC’s cost function , which ensures strong connection between the game and that the solution of the game is more likely to be achieved by a hybrid MPC (HMPC). GCV’s payoff is a linear combination of the speed payoff, headway payoff and acceleration payoff. . We use decreasing acceleration model to generate our prediction of TV’s future motion, which is utilized in both defining TV’s payoffs over the prediction horizon in the game and as the reference of the MPC. Solving the games gives the optimal gap and the target vehicle (TV). In the low level , the lane change process are divided into four stages: traveling in the current lane, leaving current lane, crossing lane marking, traveling in the target lane. The division identifies the time that SV should initiate actual lateral movement for the lateral controller and specifies the constraints HMPC should deal at each step of the MPC prediction horizon. Then the four-stage HMPC controls SV’s actual longitudinal motion and execute the lane change at the right moment. Simulations showed the GT4SMPC is able to intelligently drive SV into the selected gap and accomplish both discretionary land change (DLC) and mandatory lane change (MLC) in a dynamic situation. Human-in-the-loop driving simulation indicated that GT4SMPC can decently control the SV to complete lane changes with the presence of human drivers. Second, we propose a differential game theoretic model predictive controller (DGTMPC) to address the drawbacks of GT4SMPC. In GT4SMPC, the games are defined as table game, which indicates each players only have limited amount of choices for a specific game and such choice remain fixed during the prediction horizon. In addition, we assume a known model for traffic vehicles but in reality drivers’ preference is partly unknown. In order to allow the TV to make multiple decisions within the prediction horizon and to measure TV’s driving style on-line, we propose a differential game theoretic model predictive controller (DGTMPC). The high level of the hierarchical DGTMPC is the two-player differential lane-change Stackelberg game. We assume each player uses a MPC to control its motion and the optimal solution of leaders’ MPC depends on the solution of the follower. Therefore, we convert this differential game problem into a bi-level optimization problem and solves the problem with the branch and bound algorithm. Besides the game, we propose an inverse model predictive control algorithm (IMPC) to estimate the MPC weights of other drivers on-line based on surrounding vehicle’s real-time behavior, assuming they are controlled by MPC as well. The estimation results contribute to a more appropriate solution to the game against driver of specific type. The solution of the algorithm indicates the future motion of the TV, which can be used as the reference for the low level controller. The low level HMPC controls both the longitudinal motion of SV and his real-time lane decision. Simulations showed that the DGTMPC can well identify the weights traffic vehicles’ MPC cost function and behave intelligently during the interaction. Comparison with level-k controller indicates DGTMPC’s Superior performance

Model predictive cooperative localization control of multiple UAVs using potential function sensor constraints: a workflow to create sensor constraint based potential functions for the control of cooperative localization scenarios with mobile robots.

The global localization of multiple mobile robots can be achieved cost efficiently by localizing one robot globally and the others in relation to it using local sensor data. However, the drawback of this cooperative localization is the requirement of continuous sensor information. Due to a limited sensor perception space, the tracking task to continuously maintain this sensor information is challenging. To address this problem, this contribution is presenting a model predictive control (MPC) approach for such cooperative localization scenarios. In particular, the present work shows a novel workflow to describe sensor limitations with the help of potential functions. In addition, a compact motion model for multi-rotor drones is introduced to achieve MPC real-time capability. The effectiveness of the presented approach is demonstrated in a numerical simulation, an experimental indoor scenario with two quadrotors as well as multiple indoor scenarios of a quadrotor obstacle evasion maneuver

Proceedings of the 2009 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory

The joint workshop of the Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Karlsruhe, and the Vision and Fusion Laboratory (Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)), is organized annually since 2005 with the aim to report on the latest research and development findings of the doctoral students of both institutions. This book provides a collection of 16 technical reports on the research results presented on the 2009 workshop

Optimisation-based verification process of obstacle avoidance systems for unmanned vehicles

This thesis deals with safety verification analysis of collision avoidance systems for unmanned vehicles. The safety of the vehicle is dependent on collision avoidance algorithms and associated control laws, and it must be proven that the collision avoidance algorithms and controllers are functioning correctly in all nominal conditions, various failure conditions and in the presence of possible variations in the vehicle and operational environment. The current widely used exhaustive search based approaches are not suitable for safety analysis of autonomous vehicles due to the large number of possible variations and the complexity of algorithms and the systems. To address this topic, a new optimisation-based verification method is developed to verify the safety of collision avoidance systems. The proposed verification method formulates the worst case analysis problem arising the verification of collision avoidance systems into an optimisation problem and employs optimisation algorithms to automatically search the worst cases. Minimum distance to the obstacle during the collision avoidance manoeuvre is defined as the objective function of the optimisation problem, and realistic simulation consisting of the detailed vehicle dynamics, the operational environment, the collision avoidance algorithm and low level control laws is embedded in the optimisation process. This enables the verification process to take into account the parameters variations in the vehicle, the change of the environment, the uncertainties in sensors, and in particular the mismatching between model used for developing the collision avoidance algorithms and the real vehicle. It is shown that the resultant simulation based optimisation problem is non-convex and there might be many local optima. To illustrate and investigate the proposed optimisation based verification process, the potential field method and decision making collision avoidance method are chosen as an obstacle avoidance candidate technique for verification study. Five benchmark case studies are investigated in this thesis: static obstacle avoidance system of a simple unicycle robot, moving obstacle avoidance system for a Pioneer 3DX robot, and a 6 Degrees of Freedom fixed wing Unmanned Aerial Vehicle with static and moving collision avoidance algorithms. It is proven that although a local optimisation method for nonlinear optimisation is quite efficient, it is not able to find the most dangerous situation. Results in this thesis show that, among all the global optimisation methods that have been investigated, the DIviding RECTangle method provides most promising performance for verification of collision avoidance functions in terms of guaranteed capability in searching worst scenarios

Mixed Integer Programming-Based Semiautonomous Step Climbing of a Snake Robot Considering Sensing Strategy

We propose a control method for semiautonomous step climbing by a snake robot. Our method is based on mixed integer quadratic programming to generate the reference trajectory of the head of the snake robot online. One of the features of the method is that it determines suitable positions and time duration in which to sense the surroundings before approaching the step. Furthermore, constraints on velocity and acceleration are taken into account, so that the snake robot can securely follow the generated trajectory. Our method was applied to a snake robot equipped with a laser range finder, which is used for step detection. Experiments were performed to verify the efficacy of the method

Contextual information aided target tracking and path planning for autonomous ground vehicles

Recently, autonomous vehicles have received worldwide attentions from academic research, automotive industry and the general public. In order to achieve a higher level of automation, one of the most fundamental requirements of autonomous vehicles is the capability to respond to internal and external changes in a safe, timely and appropriate manner. Situational awareness and decision making are two crucial enabling technologies for safe operation of autonomous vehicles. This thesis presents a solution for improving the automation level of autonomous vehicles in both situational awareness and decision making aspects by utilising additional domain knowledge such as constraints and influence on a moving object caused by environment and interaction between different moving objects. This includes two specific sub-systems, model based target tracking in environmental perception module and motion planning in path planning module. In the first part, a rigorous Bayesian framework is developed for pooling road constraint information and sensor measurement data of a ground vehicle to provide better situational awareness. Consequently, a new multiple targets tracking (MTT) strategy is proposed for solving target tracking problems with nonlinear dynamic systems and additional state constraints. Besides road constraint information, a vehicle movement is generally affected by its surrounding environment known as interaction information. A novel dynamic modelling approach is then proposed by considering the interaction information as virtual force which is constructed by involving the target state, desired dynamics and interaction information. The proposed modelling approach is then accommodated in the proposed MTT strategy for incorporating different types of domain knowledge in a comprehensive manner. In the second part, a new path planning strategy for autonomous vehicles operating in partially known dynamic environment is suggested. The proposed MTT technique is utilized to provide accurate on-board tracking information with associated level of uncertainty. Based on the tracking information, a path planning strategy is developed to generate collision free paths by not only predicting the future states of the moving objects but also taking into account the propagation of the associated estimation uncertainty within a given horizon. To cope with a dynamic and uncertain road environment, the strategy is implemented in a receding horizon fashion