Model Predictive Control (MPC) has shown to be a successful method for many applications that require control. Especially in the presence of prediction uncertainty, various types of MPC offer robust or efficient control system behavior. For modeling, uncertainty is most often approximated in such a way that established MPC approaches are applicable for specific uncertainty types. However, for a number of applications, especially automated vehicles, uncertainty in predicting the future behavior of other agents is more suitably modeled by a twofold description: a high-level task uncertainty and a low-level execution uncertainty of individual tasks. In this work, we present an MPC framework that is capable of dealing with this twofold uncertainty. A scenario MPC approach considers the possibility of other agents performing one of multiple tasks, with an arbitrary probability distribution, while an analytic stochastic MPC method handles execution uncertainty within a specific task, based on a Gaussian distribution. Combining both approaches allows to efficiently handle the twofold uncertainty structure of many applications. Application of the proposed MPC method is demonstrated in an automated vehicle simulation study.
In this work, we combine {Model Predictive Control} (MPC) and Control Barrier Function (CBF) design {methods} to create a hierarchical control law for simultaneous lane-keeping (LK) and obstacle avoidance (OA): at the low level, MPC performs LK via trajectory tracking during nominal operation; and at the high level, different CBF-based safety filters that ensure both LK and OA are designed and compared across some practical scenarios. In particular, we show that Exponential Safety (ESf) and Prescribed-Time Safety (PTSf) filters, which override the MPC control when necessary, result in feasible…
Distributed model predictive control (DMPC) is often used to tackle path planning for unmanned aerial vehicle (UAV) swarms. However, it requires considerable computations on-board the UAV, leading to increased weight and power consumption. In this work, we propose to offload path planning computations to multiple ground-based computation units. As simultaneously communicating and recomputing all trajectories is not feasible for a large swarm with tight timing requirements, we develop a novel event-triggered DMPC that selects a subset of most relevant UAV trajectories to be replanned. The resul…
A Predictive Cooperative Collision Avoidance for Multi-Robot Systems Using Control Barrier Function
Harbin Institute of Technology Shenzhen（哈尔滨工业大学深圳研究院）；Southern University of Science and Technology（南方科技大学）；University of Oulu（奥卢大学）；VTT-Technical Research Centre of Finland（芬兰技术研究中心）
Trajectory Planning with Model Predictive Control for Obstacle Avoidance Considering Prediction Uncertainty
Institute of Electromobility, RPTU University Kaiserslautern-Landau（电磁移动研究所，科隆-兰道大学）；Institute of Wireless Communications and Navigation, RPTU University Kaiserslautern-Landau（无线通信与导航研究所，科隆-兰道大学）
Although extensive research in emergency collision avoidance has been carried out for straight or curved roads in a highway scenario, a general method that could be implemented for all road environments has not been thoroughly explored. Moreover, most current algorithms don't consider collision mitigation in an emergency. This functionality is essential since the problem may have no feasible solution. We propose a safe controller using model predictive control and artificial potential function to address these problems. A new artificial potential function inspired by line charge is proposed as…
Semi-Infinite Programming for Collision-Avoidance in Optimal and Model Predictive Control
Robert Bosch GmbH, Corporate Research（罗伯特·博世有限公司，企业研究）；Department of Microsystems Engineering (IMTEK), University of Freiburg（弗赖堡大学微系统工程系（IMTEK））；Fernride GmbH（费尔纳里德公司）；Institute of Automatic Control, RWTH Aachen University（亚琛工业大学自动化研究所）；Department of Mathematics, University of Freiburg（弗赖堡大学数学系）
Hamburg University of Technology（汉堡工业大学）；Institute of Mechanics and Ocean Engineering（力学与海洋工程研究所）
The goal of this thesis is to propose the combination of Control-Barrier-Functions (CBF) with Model-Predictive-Control (MPC) resulting in the novel Model-Predictive-Control-Barrier-Function (MPCBF). It can be shown, that the performance of the MPCBF surpasses the performance of the CBF due to the increased time horizon of the MPC. Moreover, the MPCBF was applied to a quadrotor, a system strongly in need of fast and predictive control. Using the MPCBF, the quadrotor was able to avoid obstacles, which the CBF failed to avoid due to the relative speed of the obstacle. The results of this work are…
In this work, a revised formulation of Chance-Constrained (CC) Model Predictive Control (MPC) is presented. The focus of this work is on the mathematical formulation of the revised CC-MPC, and the reason behind the need for its revision. The revised formulation is given in the context of sewer systems, and their weir overflow structures. A linear sewer model of the Astlingen Benchmark sewer model is utilized to illustrate the application of the formulation, both mathematically and performance-wise through simulations. Based on the simulations, a comparison of performance is done between the re…
This paper presents a three-layered hybrid collision avoidance (COLAV) system for autonomous surface vehicles, compliant with rules 8 and 13-17 of the International Regulations for Preventing Collisions at Sea (COLREGs). The COLAV system consists of a high-level planner producing an energy-optimized trajectory, a model predictive control based mid-level COLAV algorithm considering moving obstacles and the COLREGs, and the branching-course model predictive control algorithm for short-term COLAV handling emergency situations in accordance with the COLREGs. Previously developed algorithms by the …
Decentralized Control of Uncertain Multi-Agent Systems with Connectivity Maintenance and Collision Avoidance
ACCESS Linnaeus Center, School of Electrical Engineering, KTH Royal Institute of Technology（ACCESS林奈中心，电气工程学院，皇家理工学院）；KTH Center for Autonomous Systems（KTH自主系统中心）
In recent years, nonlinear model predictive control (NMPC) has been extensively used for solving automotive motion control and planning tasks. In order to formulate the NMPC problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the NMPC related optimization problem, involving a Cartesian and a Frenet coordinate frame (CCF/ FCF) in a single nonlinear program (NLP). We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints…
Control barrier functions (CBFs) recently introduced a systematic way to guarantee the system's safety through set invariance. Together with a nominal control method, it establishes a safety-critical control mechanism. The resulting safety constraints can be enforced as hard constraints in quadratic programming (QP) optimization, which rectifies the nominal control law based on the set of safe inputs. In this work, we introduce a multiple CBFs scheme which enforces several safety constraints with high relative degrees. This control structure is essential in many challenging robotic application…
In this work, an evaluation of Chance-Constrained Model Predictive Control (CC-MPC) in sewer systems over the use of the classical deterministic Model Predictive Control (MPC) is presented. The focus of this evaluation is on the avoidance of weir overflow when uncertainty is present. Furthermore, the design formulation of CC-MPC is presented with a comparison to the design of MPC. For the evaluation, a simplified model of the Barcelona sewer network case study is utilized. Our comparison shows that for sewer systems with uncertain inflows, a CC-MPC allows for better statistical guarantees for …
Research Institute of Trustworthy Autonomous Systems, SUSTech（南方科技大学可信自主系统研究院）；School of Automation, Hangzhou Dianzi University（杭州电子科技大学自动化学院）；Verimag, Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学Verimag实验室）
We design and experimentally evaluate a hybrid safe-by-construction collision avoidance controller for autonomous vehicles. The controller combines into a single architecture the respective advantages of an adaptive controller and a discrete safe controller. The adaptive controller relies on model predictive control to achieve optimal efficiency in nominal conditions. The safe controller avoids collision by applying two different policies, for nominal and out-of-nominal conditions, respectively. We present design principles for both the adaptive and the safe controller and show how each one ca…
This article considers collision avoidance (COLAV) for both static and moving obstacles using the branching-course model predictive control (BC-MPC) algorithm, which is designed for use by autonomous surface vehicles (ASVs). The BC-MPC algorithm originally only considered COLAV of moving obstacles, so in order to make the algorithm also be able to avoid static obstacles, we introduce an extra term in the objective function based on an occupancy grid. In addition, other improvements are made to the algorithm resulting in trajectories with less wobbling. The modified algorithm is verified throug…
Many systems such as autonomous vehicles and quadrotors are subject to parametric uncertainties and external disturbances. These uncertainties can lead to undesired performance degradation and safety issues. Therefore, it is important to design robust control strategies to safely regulate the dynamics of a system. This paper presents a novel framework for chance-constrained stochastic model predictive control of dynamic systems with non-Gaussian correlated probabilistic uncertainties. We develop a new stochastic Galerkin method to propagate the uncertainties using a new type of basis functions…
Efficient COLREGs-Compliant Collision Avoidance using Turning Circle-based Control Barrier Function
Mobile Robotics and Intelligence Laboratory, Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST)（移动机器人与智能实验室，机械工程系，韩国科学技术院）
We present an algorithm, based on the Differential Dynamic Programming framework, to handle trajectory optimization problems in which the horizon is determined online rather than fixed a priori. This algorithm exhibits exact one-step convergence for linear, quadratic, time-invariant problems and is fast enough for real-time nonlinear model-predictive control. We show derivations for the nonlinear algorithm in the discrete-time case, and apply this algorithm to a variety of nonlinear problems. Finally, we show the efficacy of the optimal-horizon model-predictive control scheme compared to a sta…
In this paper we propose a technique that assigns obstacles to clusters used for collision avoidance via Mixed-Integer Programming. This strategy enables a reduction in the number of binary variables used for collision avoidance, thus entailing a decrease in computational cost, which has been a hindrance to the application of Model Predictive Control approaches with Mixed-Integer Programming formulations in real-time. Moreover, the assignment of obstacles to clusters and the sizes of the clusters are decided within the same optimization problem that performs the trajectory planning, thus yield…
Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control…
Kiel University（基尔大学）；AVL Software and Functions GmbH（AVL软件与功能有限公司）
A path-following collision-avoidance model predictive control (MPC) method is proposed which approximates obstacle shapes as convex polygons. Collision-avoidance is ensured by means of the signed distance function which is calculated efficiently as part of the MPC problem by making use of a dual formulation. The overall MPC problem can be solved by standard nonlinear programming (NLP) solvers. The dual signed distance formulation yields, besides the (dual) collision-avoidance constraints, norm, and consistency constraints. A novel approach is presented that combines the arising norm equality w…
Efficient Collision-Avoidance Constraints for Ellipsoidal Obstacles in Optimal Control: Application to Path-Following MPC and UAVs
Institute of Engineering and Computational Mechanics, University of Stuttgart（工程与计算力学研究所，斯图加特大学）；Chair of Systems Modeling and Simulation, Saarland University（系统建模与仿真教授团，萨尔兰大学）；Department of Mechanical Engineering, LUT University（机械工程系，卢霍斯大学）
Dynamic Bipedal MPC with Foot-level Obstacle Avoidance and Adjustable Step Timing
Mechanical Engineering Department at the FAMU-FSU College of Engineering（佛罗里达州立大学工程学院机械工程系）；FAMU-FSU College of Engineering（佛罗里达大学-萨拉姆斯学院工程学院）；Toyota Research Institute（丰田研究院）；Ford Motor Company（福特汽车公司）
