Time-optimal Model Predictive Control Research Articles

Safe-by-construction autonomous vehicle overtaking using control barrier functions and model predictive control

Ensuring safety for vehicle overtaking systems is one of the most fundamental and challenging tasks in autonomous driving. This task is particularly intricate when the vehicle must not only overtake its front vehicle safely but also consider the presence of potential opposing vehicles in the opposite lane that it will temporarily occupy. In order to tackle the overtaking task in such challenging scenarios, we introduce a novel integrated framework tailored for vehicle overtaking manoeuvres. Our approach integrates the theories of varying-level control barrier functions (CBF) and time-optimal model predictive control (MPC). The main feature of our proposed overtaking strategy is that it is safe-by-construction, which enables rigorous mathematical proof and validation of the safety guarantees. We show that the proposed framework is applicable when the opposing vehicle is either fully autonomous or driven by human drivers. To demonstrate our framework, we perform a set of simulations for overtaking scenarios under different settings. The simulation results show the superiority of our framework in the sense that it ensures collision-free and achieves better safety performance compared with the standard MPC-based approach without safety guarantees.

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors Considering Current and Torque Constraints

In various permanent magnet synchronous motor (PMSM) drive applications the torque dynamics are an important performance criterion. Here, time-optimal control (TOC) methods can be utilized to achieve highest control dynamics. Applying state-of-the-art TOC methods leads to unintended overcurrents and torque over- and undershoots during transient operation. To prevent these unintended control characteristics while still achieving TOC performance the time-optimal model predictive control (TO-MPC) is proposed in this work. The TO-MPC contains a reference pre-rotation (RPR) and a continuous control set model predictive flux control (CCS-MPFC). By applying Pontryagin's maximum principle, the TOC solution trajectories for states and inputs of the PMSM are determined neglecting current and torque limits. With the TOC solution, a flux linkage reference for the CCS-MPFC is calculated that corresponds to a pre-rotation of the operating point in the stator-fixed coordinate system. This pre-rotated flux linkage reference is reached in minimum time without overcurrents and torque over- as well as undershoots by incorporating current and torque limits as time-varying softened state constraints into the CCS-MPFC. Simulative and experimental investigations for linearly and nonlinearly magnetized PMSMs in the whole speed and torque range show that, compared to state-of-the-art TOC methods, overcurrents and torque over- as well as undershoots are prevented by the proposed TO-MPC.

Analysis of Model Predictive Intersection Control for Autonomous Vehicles

Autonomous vehicles are in the main focus for automotive companies and urban traffic engineers as well. As their penetration rate in traffic becomes more and more pronounced due to improvement in sensor technologies and the corresponding infrastructure, new methods for autonomous vehicle controls become a necessity. For instance, autonomous vehicles can improve the performance of urban traffic and prevent the formation of congestions with the usage of Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication based control methods. One of the key area for improvement is centralized intersection control for autonomous vehicles, by which traveling times can be reduced and efficiency of traffic flow can be improved, while safety of passengers can be guaranteed through constraints built in the centralized design. The paper presents the analysis of a Model Predictive Control (MPC) method for the coordination of autonomous vehicles at intersections by comparing it with an offline constraint optimization considering time and energy optimal intervention of vehicles. The analysis has been evaluated in high-fidelity simulation environment CarSim, where the speed trajectories, traveling times and energy consumptions have been compared for the different methods. The simulations show that the proposed time-optimal MPC intersection control method results in similar traveling times of that given by the time-optimal offline constraint optimization, while the energy optimal optimization re-quires significantly more time for the autonomous vehicle to achieve. Due to the possibility of a congestion forming in the latter case, the proposed centralized MPC method is more applicable in real traffic scenarios.

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors in the Whole Speed and Modulation Range Considering Current and Torque Limits

Time-Optimal Model Predictive Control of Permanent Magnet Synchronous Motors in the Whole Speed and Modulation Range Considering Current and Torque Limits

Guided Time-Optimal Model Predictive Control of a Multi-Rotor

Time-optimal control of a multi-rotor remains an open problem due to the under-actuation and nonlinearity of its dynamics, which make it difficult to solve this problem directly. In this paper, the time-optimal control problem of the multi-rotor is studied. Firstly, a thrust limit optimal decomposition method is proposed, which can reasonably decompose the limited thrust into three directions according to the current state and the target state. As a result, the thrust limit constraint is decomposed as a linear constraint. With the linear constraint and decoupled dynamics, a time-optimal guidance trajectory can be obtained. Then, a cost function is defined based on the time-optimal guidance trajectory, which has a quadratic form and can be used to evaluate the time-optimal performance of the system outputs. Finally, based on the cost function, the time-optimal control problem is reformulated as an MPC (Model Predictive Control) problem. The experimental results demonstrate the feasibility and validity of the proposed methods.

Efficient Bang-Bang Model Predictive Control for Quadcopters

Time-optimal model predictive control is important for achieving fast racing drones but is computationally intensive and thereby rarely used onboard small quadcopters with limited computational resources. In this work, we simplify the optimal control problem (OCP) of the position loop for several maneuvers by exploiting the fact that the solution resembles a so-called ‘bang-bang’ in the critical direction, where only the switching time needs to be found. The noncritical direction uses a ‘minimum effort’ approach. The control parameters are obtained through bisection search schemes on an analytical path prediction model. The approach is compared with a classical PID controller and theoretical time-optimal trajectories in simulations. We explain the effects of the OCP simplifications and introduce a method of mitigating one of these effects. Finally, we have implemented the ‘bang-bang’ controller as a model predictive controller (MPC) onboard a Parrot Bebop and performed indoor flights to compare the controller’s performance to a PID controller. We show that the light novel controller outperforms the PID controller in waypoint-to-waypoint flight while requiring only minimal knowledge of the quadcopter’s dynamics.

GTO-MPC-Based Target Chasing Using a Quadrotor in Cluttered Environments

This article addresses the challenging problem of chasing an escaping target using a quadrotor in cluttered environments. To tackle these challenges, we propose a guided time-optimal model predictive control (GTO-MPC)-based practical framework to generate chasing trajectories for the quadrotor. A jerk limited approach is first adopted to find a time-optimal jerk limited trajectory (JLT), an initial reference for the quadrotor to track, without taking into account surrounding obstacles and potential threats. An MPC-based replanning framework is then applied to approximate the JLT together with the consideration of other issues such as flight safety, line-of-sight maintenance, and deadlock avoidance. Combined with a neural network, the proposed GTO-MPC framework can efficiently generate chasing trajectories that guarantee flight smoothness and kinodynamic feasibility. Our simulation and actual experimental results show that the proposed technique is highly effective.

An Approach to Time Optimal Model Predictive Control for Robot Brachiation with Probabilistic Selection of Time Horizon

An Approach to Time Optimal Model Predictive Control for Robot Brachiation with Probabilistic Selection of Time Horizon

Time optimal model predictive control for linear systems based on ellipsoidal and polytopic sets

Time optimal model predictive control (MPC) strategies are investigated in this paper. We first derive a series of controllable sets described by ellipsoids or convex polytopes offline, then obtain the control input that can steer initial state into the terminal set in the shortest time steps by solving an online optimisation problem with lower computational burden. The constraints of online optimisation problem are determined by the controllable sets. We give the methods to calculate the ellipsoidal controllable sets for linear time-invariant systems and linear time-varying systems, respectively, and propose a new method to calculate the polytopic controllable sets for linear time-varying systems. The recursive feasibility of online optimisation problem and the stability of the closed-loop system can be guaranteed. Numerical examples show that the algorithms work well.

Modelling minimum-time manoeuvering with global optimisation of local receding horizon control

In this paper, we explore the notion that a human driver uses a receding horizon model predictive control (MPC) scheme for minimum-time manoeuvering. However, MPC is an inherently sub-optimal control scheme because not all future information is incorporated into its finite preview horizon. In many practical applications, this sub-optimality is tolerated as the solution is sufficiently close to optimal. However, it is known that professional drivers have the ability to learn driving circuits and exploit its features to minimise their global manoeuvering time. In this paper, we will model their process with a cascaded optimisation structure. Therein, the inner-loop features a local MPC scheme tasked with finding the control inputs that achieve a blended objective of minimising time and maximising velocity in each preview horizon/distance. The outer loop of this cascaded structure computes the best set of weights for the two components of the local objectives in order to minimise the global manoeuvering time. The proposed cascaded optimisation and control approach is compared against a straight-forward fixed-cost time optimal MPC applied to minimum-time manoeuvering over two well-known race courses. The paper also includes an extended literature review and details of the computational formulation of the model approach.

Classical and modern methods for time-constrained energy optimal motion – Application to a badminton robot

Two control approaches are presented to improve the energy efficiency of a robot which has to perform point-to-point motions during a fixed time interval. One is called Proximate Energy Optimal Servo (PEOS) and the other is called Energy-Optimal Model Predictive Control (EOMPC). The PEOS approach is based on the Proximate Time Optimal Servo (PTOS) control algorithm whose parameters are optimized in order to achieve energy efficient behavior. The EOMPC approach developed based on the Time-Optimal Model Predictive Control (TOMPC) approach achieves energy optimal performance by minimizing the energy losses in the object function. The two developed approaches are applied to a robot playing badminton and compared to two existing control approaches: the Proximate Time Optimal Servo (PTOS) and the Time-Optimal Model Predictive Control (TOMPC). The robot is still able to intercept most of the opponent shuttles on time, while a significant reduction of the energy consumption is demonstrated in both cases.

A model predictive control approach for time optimal point-to-point motion control

This paper presents a new model predictive control method for time-optimal point-to-point motion control of mechatronic systems. The formulation of time-optimal behavior within the model predictive control framework and the structure of the underlying optimization problem are discussed and modifications are presented in order to decrease the computational load of the numerical solution method such that sampling rates in the millisecond range and long prediction horizons for large point-to-point motions are feasible. An extensive experimental validation on a linear motor drive and an overhead crane setup demonstrates the advantages of the developed time-optimal model predictive control approach in comparison with traditional model predictive control.

Model predictive control for time-optimal point-to-point motion control

AbstractThis paper presents a time-optimal model predictive control approach, which is a new type of MPC approach for motion systems that aims at performing time-optimal point-to-point motions. It is shown how the structure of the underlying optimal control problem can be exploited such that it can be solved in real-time at a sampling rate of 200 Hz. Numerical and experimental validation on a linear motor drive system and comparison with traditional MPC and linear control techniques clearly demonstrate the advantages of time-optimal model predictive control.