Georg Schildbach

Dynamic Vehicle Redistribution and Online Price Incentives in Shared Mobility Systems

This paper considers the efficient operation of shared mobility systems via the combination of intelligent routing decisions for staff-based vehicle redistribution and real-time price incentives for customers. The approach is applied to Londons Barclays Cycle Hire scheme, which the authors have simulated based on historical data. Using model-based predictive control principles, dynamically varying rewards are computed and offered to customers carrying out journeys, based on the current and predicted state of the system. The aim is to encourage them to park bicycles at nearby underused stations, thereby reducing the expected cost of redistributing them using dedicated staff. In parallel, routing directions for redistribution staff are periodically recomputed using a model-based heuristic. It is shown that it is possible to trade off reward payouts to customers against the cost of hiring staff to redistribute bicycles, in order to minimize operating costs for a given desired service level.

The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations

Many practical applications in control require that constraints on the inputs and states of the system are respected, while some performance criterion is optimized. In the presence of model uncertainties or disturbances, it is often sufficient to satisfy the state constraints for at least a prescribed share of the time, such as in building climate control or load mitigation for wind turbines. For such systems, this paper presents a new method of Scenario-Based Model Predictive Control (SCMPC). The basic idea is to optimize the control inputs over a finite horizon, subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and/or disturbances. Previous SCMPC approaches have suffered from a substantial gap between the rate of constraint violations specified in the optimal control problem and that actually observed in closed-loop operation of the controlled system. This paper identifies the two theoretical explanations for this gap. First, accounting for the special structure of the optimal control problem leads to a substantial reduction of the problem dimension. Second, the probabilistic constraints have to be interpreted as average-in-time, rather than pointwise-in-time. Based on these insights, a novel SCMPC method can be devised for general linear systems with additive and multiplicative disturbances, for which the number of scenarios is significantly reduced. The presented method retains the essential advantages of the general SCMPC approach, namely a low computational complexity and the ability to handle arbitrary probability distributions. Moreover, the computational complexity can be adjusted by a sample-and-remove strategy.

Automated Driving The Role of Forecasts and Uncertainty - A Control Perspective

Abstract Driving requires forecasts. Forecasted movements of objects in the driving scene are uncertain. Inevitably, decision and control algorithms for autonomous driving need to cope with such uncertain forecasts. In assisted driving, the uncertainty in the human/vehicle interaction further increases the complexity of the control design task. Our research over the past ten years has focused on control design methods which systematically handle uncertain forecasts for autonomous and semi-autonomous vehicles. This paper presents an overview of our findings and discusses relevant aspects of our recent results.

Kinematic and dynamic vehicle models for autonomous driving control design

We study the use of kinematic and dynamic vehicle models for model-based control design used in autonomous driving. In particular, we analyze the statistics of the forecast error of these two models by using experimental data. In addition, we study the effect of discretization on forecast error. We use the results of the first part to motivate the design of a controller for an autonomous vehicle using model predictive control (MPC) and a simple kinematic bicycle model. The proposed approach is less computationally expensive than existing methods which use vehicle tire models. Moreover it can be implemented at low vehicle speeds where tire models become singular. Experimental results show the effectiveness of the proposed approach at various speeds on windy roads.

On the sample size of randomized MPC for chance-constrained systems with application to building climate control

We consider Stochastic Model Predictive Control (SMPC) for constrained linear systems with additive disturbance, under affine disturbance feedback (ADF) policies. One approach to solve the chance-constrained optimization problem associated with the SMPC formulation is randomization, where the chance constraints are replaced by a number of sampled hard constraints, each corresponding to a disturbance realization. The ADF formulation leads to a quadratic growth in the number of decision variables with respect to the prediction horizon, which results in a quadratic growth in the sample size. This leads to computationally expensive problems with solutions that are conservative in terms of both cost and violation probability. We address these limitations by establishing a bound on the sample size which scales linearly in the prediction horizon. The new bound is obtained by explicitly computing the maximum number of active constraints, leading to significant advantages both in terms of computational time and conservatism of the solution. The efficacy of the new bound relative to the existing one is demonstrated on a building climate control case study.

Randomized Model Predictive Control for stochastic linear systems

This paper is concerned with the design of state-feedback control laws for linear time invariant systems that are subject to stochastic additive disturbances, and probabilistic constraints on the states. The design is based on a stochastic Model Predictive Control (MPC) approach, for which a randomization technique is applied in order to find a suboptimal solution to the underlying, generally non-convex chance constrained program. The proposed method yields a linear or quadratic program to be solved online at each time step, whose complexity is the same as that of a nominal MPC problem, i.e. if no disturbances were present. Furthermore, it is shown how the quality of the sub-optimal solution can be improved through a procedure for the removal of sampled constraints a-posteriori, at the price of increased online computation efforts. Finally, this randomized approach can be combined with further constraint tightening, in order to guarantee recursive feasibility for the closed loop system.

Scenario model predictive control for lane change assistance on highways

This paper presents a new algorithm for detecting the safety of lane changes on highways and for computing safe lane change trajectories. This task is considered as a building block for driver assistance systems and autonomous cars. The presented algorithm is based on recent results in Scenario Model Predictive Control (SCMPC). It accounts for the uncertainty in the traffic environment via a small number of future scenarios, which can be generated by any model-based or data-based approach. The paper describes the SCMPC design as well as the integration with scenario-based traffic predictions. The design procedure is simple and can be generalized to other control situations. An extensive case study demonstrates the effectiveness of the proposed SCMPC algorithm and its performance in lane change situations.

Scenario-based model predictive control for multi-echelon supply chain management

Policies for managing multi-echelon supply chains can be considered mathematically as large-scale dynamic programs, affected by uncertainty and incomplete information. Except for a few special cases, optimal solutions are computationally intractable for systems of realistic size. This paper proposes a novel approximation scheme using scenario-based model predictive control (SCMPC), based on recent results in scenario-based optimization. The presented SCMPC approach can handle supply chains with stochastic planning uncertainties from various sources (demands, lead times, prices, etc.) and of a very general nature (distributions, correlations, etc.). Moreover, it guarantees a specified customer service level, when applied in a rolling horizon fashion. At the same time, SCMPC is computationally efficient and able to tackle problems of a similar scale as manageable by deterministic optimization. For a large class of supply chain models, SCMPC may therefore offer substantial advantages over robust or stochastic optimization.

A collision avoidance system at intersections using Robust Model Predictive Control

Collisions at intersections account for about 40% of all car accidents and for about 20% of all traffic fatalities in the United States. The main cause is human error in recognition and decision making. Active safety systems have thus a great potential for increasing vehicle safety at intersections. They may issue warnings to the driver or assume control of the vehicle in critical situations. Most approaches in current research rely on the assumption that all vehicles at the intersection are controllable, and/or they can be coordinated by a central intersection manager. This paper considers the case of a single controllable ego vehicle surrounded by several uncontrollable target vehicles, without communication. Only a map with the current position and velocity of the target vehicles are assumed to be known, but no pre-defined crossing order is given. A Robust Model Predictive Control strategy is designed for finding safe gaps in the crossing traffic, and for planning optimal trajectories to maximize the ego vehicles efficiency and driver comfort. It is shown that its performance can be enhanced by Affine Disturbance Feedback. The algorithm is tested in several simulation scenarios and implemented on a test vehicle for experimental validation.

Stochastic predictive control for lane keeping assistance systems using a linear time-varying model

This paper presents a new controller for prevention of unintended roadway departures using model predictive control (MPC). The uncertainty with the drivers behavior is taken into account as the Gaussian disturbance. Correspondingly, we impose a lower bound on the probability of the vehicle remaining within the lane. Using current information of the vehicle and predicted steering of the driver, a linear time-varying (LTV) model of the human-vehicle system is obtained on-line through a successive linearization approach. The probabilistic safety constraints are converted into tightened constraints on the states of the LTV model by computing the evolution of the disturbance. Consequently, the predictive control problem is formulated as a quadratic program. The controller corrects the drivers steering, wherever there is a risk of unintended roadway departure, to keep the vehicle within the lane. Simulations and experiments implemented on a passenger vehicle were performed. The results indicate that the proposed controller improves safety performance compared to previous works.