Guaranteeing constraint satisfaction is challenging in imitation learning (IL), particularly in tasks that require operating near a system’s handling limits. Traditional IL methods, such as Behavior Cloning (BC), often struggle to enforce constraints, leading to suboptimal performance in high-precision tasks. In this paper, we present a simple approach to incorporating safety into the IL objective. Through simulations, we empirically validate our approach on an autonomous racing task with both full-state and image feedback, demonstrating improved constraint satisfaction and greater consistency in task performance compared to BC.

This work presents a novel Learning Model Predictive Control (LMPC) strategy for autonomous racing at the handling limit that can iteratively explore and learn unknown dynamics in high-speed operational domains. We start from existing LMPC formulations and modify the system dynamics learning method. In particular, our approach uses a nominal, global, nonlinear, physics-based model with a local, linear, data-driven learning of the error dynamics. We conducted experiments in simulation and on 1/10th scale hardware, and deployed the proposed LMPC on a full-scale autonomous race car used in the Indy Autonomous Challenge (IAC) with closed loop experiments at the Putnam Park Road Course in Indiana, USA. The results show that the proposed control policy exhibits improved robustness to parameter tuning and data scarcity. Incremental and safety-aware exploration toward the limit of handling and iterative learning of the vehicle dynamics in high-speed domains is observed both in simulations and experiments.

This paper addresses the eco-driving problem for connected vehicles on urban roads, considering localization uncertainty. Eco-driving is defined as longitudinal speed planning and control on roads with the presence of a sequence of traffic lights. We solve the problem by using a data-driven model predictive control (MPC) strategy. This approach involves learning a cost-to-go function and constraints from state-input data. The cost-to-go function represents the remaining energy-to-spend from the given state, and the constraints ensure that the controlled vehicle passes the upcoming traffic light timely while obeying traffic laws. The resulting convex optimization problem has a short horizon and is amenable for real-time implementations. We demonstrate the effectiveness of our approach through real-world vehicle experiments. Our method demonstrates 12% improvement in energy efficiency compared to the traditional approaches, which plan longitudinal speed by solving a long-horizon optimal control problem and track the planned speed using another controller, as evidenced by vehicle experiments.

We propose a hierarchical architecture designed for scalable real-time Model Predictive Control (MPC) in complex, multi-modal traffic scenarios. This architecture comprises two key components: 1) RAID-Net, a novel attention-based Recurrent Neural Network that predicts relevant interactions along the MPC prediction horizon between the autonomous vehicle and the surrounding vehicles using Lagrangian duality, and 2) a reduced Stochastic MPC problem that eliminates irrelevant collision avoidance constraints, enhancing computational efficiency. Our approach is demonstrated in a simulated traffic intersection with interactive surrounding vehicles, showcasing a 12x speed-up in solving the motion planning problem. A video demonstrating the proposed architecture in multiple complex traffic scenarios can be found here: https://youtu.be/-pRiOnPb9_c. GitHub: https://github.com/MPC-Berkeley/hmpc_raidnet

In this work, we propose a numerical method for the solution of local generalized Nash equilibria (GNE) for the class of open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration and is locally convergent. Central to the effectiveness of our approach is a non-monotonic line search method and a novel merit function for SQP step acceptance which helps to improve solver convergence beyond the local neighborhood of a GNE. We demonstrate the effectiveness of the algorithm in the context of car racing, where we see up to 32% improvement of success rate when comparing against a recent solution approach for dynamic games. We also make our code available at https://github.com/zhu-edward/DGSQP.

In head-to-head racing, performing tightly con-strained, but highly rewarding maneuvers, such as overtaking, require an accurate model of interactive behavior of the opposing target vehicle (TV). We propose to construct a prediction model given data of the TV from previous races. In particular, a one-step Gaussian process (GP) model is trained on closed-loop interaction data to learn the behavior of a TV driven by an unknown policy. Predictions of the nominal trajectory and associated uncertainty are rolled out via a sampling-based approach and are used in a model predictive control (MPC) policy for the ego vehicle in order to intelligently trade-off between safety and performance when racing against a TV. In a Monte Carlo study, we compare the GP-based predictor in closed-loop with the MPC policy against several predictors from literature and observe that the GP-based predictor achieves similar win rates while maintaining safety in up to 3x more races. Through experiments, we demonstrate the approach in real-time on a 1/10th scale racecar platform operating at speeds of around 2.8 m/s, and show a significant level of improvement when using the GP-based predictor over a baseline MPC predictor. Videos of the experiments can be found at https://voutu.be/KMSs4ofDfIs.

This work presents a novel hierarchical approach to increase Battery Electric Buses (BEBs) utilization in transit fleets. The proposed approach relies on three key components. A learning-based BEB digital twin cloud platform is used to accurately predict BEB charge consumption on a per vehicle, per driver, and per route basis, and accurately predict the time-to-charge BEB batteries to any level. These predictions are then used by a Predictive Block Assignment module to maximize the BEB fleet utilization. This module computes the optimal BEB daily assignment and charge management strategy. A Depot Parking and Charging Queue Management module is used to autonomously park and charge the vehicles based on their charging demands. The paper discusses the technical approach and benefits of each level in the architecture and concludes with a realistic simulations study. The study shows that if our approach is employed BEB fleet utilization can increase by a 50% compared to state-of-the-art methods.

This paper presents a novel energy-efficient motion planning algorithm for Connected Autonomous Vehicles (CAVs) on urban roads. The approach utilizes two components: a decision-making algorithm and an optimization-based trajectory planner. The decision-making algorithm leverages Signal Phase and Timing (SPaT) information from connected traffic lights to select a lane with the aim of reducing energy consumption. The algorithm is based on a heuristic rule which is learned from human driving data. The optimization-based trajectory planner generates a safe, smooth, and energy-efficient trajectory toward the selected lane. The proposed strategy is experimentally evaluated in a Vehicle-in-the-Loop (VIL) setting, where a real test vehicle receives SPaT information from both real and virtual traffic lights and autonomously drives on a testing site, while the surrounding vehicles are simulated. The results demonstrate that the use of SPaT information in autonomous driving leads to improved energy efficiency, with the proposed strategy saving 37.1% energy consumption compared to a lane-keeping algorithm.

This work presents a distributed algorithm for resolving cooperative multi-vehicle conflicts in highly constrained spaces. By formulating the conflict resolution problem as a Multi-Agent Reinforcement Learning (RL) problem, we can train a policy offline to drive the vehicles towards their destinations safely and efficiently in a simplified discrete environment. During the online execution, each vehicle first simulates the interaction among vehicles with the trained policy to obtain its strategy, which is used to guide the computation of a reference trajectory. A distributed Model Predictive Controller (MPC) is then proposed to track the reference while avoiding collisions. The preliminary results show that the combination of RL and distributed MPC has the potential to guide vehicles to resolve conflicts safely and smoothly while being less computationally demanding than the centralized approach.

This article proposes a hierarchical learning architecture for safe data-driven control in unknown environments. We consider a constrained nonlinear dynamical system and assume the availability of state-input trajectories solving control tasks in different environments. In addition to task-invariant system state and input constraints, a parameterized environment model generates task-specific state constraints, which are satisfied by the stored trajectories. Our goal is to use these trajectories to find a safe and high-performing policy for a new task in a new, unknown environment. We propose using the stored data to learn generalizable control strategies. At each time step, based on a local forecast of the new task environment, the learned strategy consists of a target region in the state space and input constraints to guide the system evolution to the target region. These target regions are used as terminal sets by a low-level model predictive controller. We show how toi)design the target sets from past data and thenii)incorporate them into a model predictive control scheme with shifting horizon that ensures safety of the closed-loop system when performing the new task. We prove the feasibility of the resulting control policy, and apply the proposed method to robotic path planning, racing, and computer game applications.Note to Practitioners—This paper was motivated by the challenge of designing safe controllers for autonomous systems navigating through new environments. We consider scenarios where trajectory data from control tasks in different environments is available to the control designer. Possible applications include autonomous vehicles racing on new tracks or robotic manipulators performing tasks in the presence of new obstacles. Existing approaches to model-based control design for new environments generally use trajectory libraries, systematically adapting stored trajectories to the constraints of the new environment. This typically requires a priori knowledge of the entire task environment as well as resources to store and maintain the growing library. This paper suggests a new hierarchical control approach, in which stored trajectories are used to learn high-level strategies that can be applied while solving the new task. The strategies are learned offline, and only the parameterized strategy function needs to be stored for online control. Strategies only require knowledge of the nearby task environment, and provide navigation guidelines for the system. In this paper we show how to find such strategies from previous task data and how to integrate them into a low-level controller to safely and efficiently solve the new task. We also show how to adapt the modular framework as needed for a user’s desired application. Simulation experiments in robotic manipulator, autonomous vehicle, and computer game examples suggest that our approach can be used in a wide range of applications. In future research, we will address how to adapt the method for time-varying or stochastic environments.

We present a hierarchical control approach for maneuvering an autonomous vehicle (AV) in tightly-constrained environments where other moving AVs and/or human driven vehicles are present. A two-level hierarchy is proposed: a high-level data-driven strategy predictor and a lower-level model-based feedback controller. The strategy predictor maps an encoding of a dynamic environment to a set of high-level strategies via a neural network. Depending on the selected strategy, a set of time-varying hyperplanes in the AV’s position space is generated online and the corresponding halfspace constraints are included in a lower-level model-based receding horizon controller. These strategy-dependent constraints drive the vehicle towards areas where it is likely to remain feasible. Moreover, the predicted strategy also informs switching between a discrete set of policies, which allows for more conservative behavior when prediction confidence is low. We demonstrate the effectiveness of the proposed data-driven hierarchical control framework in a two-car collision avoidance scenario through simulations and experiments on a 1/10 scale autonomous car platform where the strategy-guided approach outperforms a model predictive control baseline in both cases.

In this paper, we propose a leader-follower hierarchical strategy for two robots collaboratively transporting an object in a partially known environment with obstacles. Both robots sense the local surrounding environment and react to obstacles in their proximity. We consider no explicit communication, so the local environment information and the control actions are not shared between the robots. At any given time step, the leader solves a model predictive control (MPC) problem with its known set of obstacles and plans a feasible trajectory to complete the task. The follower estimates the inputs of the leader and uses a policy to assist the leader while reacting to obstacles in its proximity. The leader infers obstacles in the follower’s vicinity by using the difference between the predicted and the real-time estimated follower control action. A method to switch the leader-follower roles is used to improve the control performance in tight environments. The efficacy of our approach is demonstrated with detailed comparisons to two alternative strategies, where it achieves the highest success rate, while completing the task fastest.

First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges: manual hyperparameter tuning and convergence time to high-accuracy solutions. To address these, we explore how Reinforcement Learning (RL) can learn a policy to tune parameters to accelerate convergence. In experiments with well-known QP benchmarks we find that our RL policy, RLQP, significantly outperforms state-of-the-art QP solvers by up to 3x. RLQP generalizes surprisingly well to previously unseen problems with varying dimension and structure from different applications, including the QPLIB, Netlib LP and Maros-M{\'e}sz{\'a}ros problems. Code, models, and videos are available at https://berkeleyautomation.github.io/rlqp/.

Plug-in electric vehicles (PEVs) have the highest promise for dramatically reducing transportation emissions. No other option has comparable emission reduction potential or as a promising pathway. Still, PEVs can offer more than green transportation. In particular, their onboard storage can further serve the society by providing an energy buffer to increase the reliability, affordability, and sustainability of electric services. These benefits are only achievable by fully exploiting the multifaceted flexibility provided by PEVs' mobility, charging adaptability, and bidirectional flow of power, as well as adopting effective decision-making and control algorithms, while minding the likely unfavorable side effects, such as shortened battery life span. This work takes a closer look at different elements of this puzzle. The main subject of this survey is behind the meter energy management with vehicle to building (V2B). We focus on different V2B application ideas and review energy management methods in smart buildings with V2B integration. Recent findings on battery capacity fade resulting from the bidirectional flow of power and extra discharging cycles with V2B are reviewed, and the methods for integrating the battery degradation in energy management formulation are discussed. Finally, the main findings of this review and research gaps are summarized and clarified.

Connected and automated vehicles (CAVs) have the potential to improve the safety of automated driving by utilizing increased awareness about their surroundings in real time vehicle control. In this paper we propose a framework for a shared perception system suitable for CAVs and explain the algorithms used in the system. Finally, we experimentally demonstrate the benefit of our shared perception system for automated vehicles in uncertain environments.

We investigate the problem of predicting driver behavior in parking lots, an environment which is less structured than typical road networks and features complex, interactive maneuvers in a compact space. Using the CARLA simulator, we develop a parking lot environment and collect a dataset of human parking maneuvers. We then study the impact of model complexity and feature information by comparing a multi-modal Long Short-Term Memory (LSTM) prediction model and a Convolution Neural Network LSTM (CNN-LSTM) to a physics-based Extended Kalman Filter (EKF) baseline. Our results show that 1) intent can be estimated well (roughly 85% top-1 accuracy and nearly 100% top-3 accuracy with the LSTM and CNN-LSTM model); 2) knowledge of the human driver's intended parking spot has a major impact on predicting parking trajectory; and 3) the semantic representation of the environment improves long term predictions.

This article focuses on the speed planning problem for connected and automated vehicles (CAVs) communicating to traffic lights. The uncertainty of traffic signal timing for signalized intersections on the road is considered. The eco-driving problem is formulated as a data-driven chance-constrained robust optimization problem. Effective red-light duration (ERD) is defined as a random variable, and describes the feasible passing time through the signalized intersections. Usually, the true probability distribution for ERD is unknown. Consequently, a data-driven approach is adopted to formulate chance constraints based on empirical sample data. This incorporates robustness into the eco-driving control problem with respect to uncertain signal timing. Dynamic programming (DP) is employed to solve the optimization problem. The simulation results demonstrate that the proposed method can generate optimal speed reference trajectories with 40% less vehicle fuel consumption, while maintaining the arrival time at a similar level compared to a modified intelligent driver model (IDM). The proposed control approach significantly improves the controller's robustness in the face of uncertain signal timing, without requiring to know the distribution of the random variable a priori.

As autonomous vehicles (AVs) inch closer to reality, a central requirement for acceptance will be earning the trust of humans in everyday driving situations. In particular, the interaction between AVs and pedestrians is of high importance, as every human is a pedestrian at some point of the day. This paper considers the interaction of a pedestrian and an autonomous vehicle at a mid-block, unsignalized intersection where there is ambiguity over when the pedestrian should cross and when and how the vehicle should yield. By modeling pedestrian behavior through the concept of gap acceptance, the authors show that a hybrid controller with just four distinct modes allows an autonomous vehicle to successfully interact with a pedestrian across a continuous spectrum of possible crosswalk entry behaviors. The controller is validated through extensive simulation and compared to an alternate POMDP solution and experimental results are provided on a research vehicle for a virtual pedestrian.

This paper presents a novel approach in train control systems based on the concept called virtual coupling or train convoys. This approach follows the recent developments in the field of safe platooning of autonomous vehicles. We use a decentralized model predictive control (MPC) framework for each train participating in a convoy formation. Control designs for the leading and following trains are presented. An optimal control formulation for both controllers is used and its design relies on a numeric solution of a finite horizon optimal control problem. This paper compares the proposed method with alternative control strategies including the well-studied moving block train control concept. A study of a metro line has been chosen as a first analysis for this control approach. The simulation results for this kind of railway lines demonstrate better performance and the benefits of this new concept versus the moving block system. We show that the virtual coupling concept substantially reduces headway and distance between trains while guaranteeing safe separation between two consecutive trains at any instant.

This paper presents a human-centered risk assessment algorithm using vehicular communication for application to an automated driving vehicle. Vehicle-to-vehicle (V2V) wireless communication has been implemented and fused with a radar sensor to obtain the prediction of the remote vehicle's motion. Based on the predicted behavior of remote vehicles, a collision risk and a human reaction time are determined for a human-centered active safety control intervention moment. The human-centered risk assessment algorithm has been incorporated into a collision avoidance algorithm to monitor threat vehicles ahead and to find the best intervention point. Effects of the vehicular communication on a perception and a control performance are investigated. The performance of the proposed algorithm has been investigated via computer simulations and vehicle tests. It has been shown from both simulations and vehicle tests that the proposed human-centered risk assessment algorithm with V2V communication decides a proper active safety intervention moment by reducing the chances of over/underestimate of a conventional radar-only system.

We study an algorithm that allows a vehicle to autonomously change lanes in a safe but personalized fashion without the driver's explicit initiation (e.g. activating the turn signals). Lane change initiation in autonomous driving is typically based on subjective rules, functions of the positions and relative velocities of surrounding vehicles. This approach is often arbitrary, and not easily adapted to the driving style preferences of an individual driver. Here we propose a data-driven modeling approach to capture the lane change decision behavior of human drivers. We collect data with a test vehicle in typical lane change situations and train classifiers to predict the instant of lane change initiation with respect to the preferences of a particular driver. We integrate this decision logic into a model predictive control (MPC) framework to create a more personalized autonomous lane change experience that satisfies safety and comfort constraints. We show the ability of the decision logic to reproduce and differentiate between two lane changing styles, and demonstrate the safety and effectiveness of the control framework through simulations.

This paper presents the design of a driver steering assistance system, which provides a corrective torque in order to guide the driver. While designing such a system, it is important to consider the interactions since the driver modifies the transfer function from the control input to the output of interest during a shared steering task. The novelty of our approach lies in the formulation of the predictive controller, which employs a model of the driver-in-the-loop steering dynamics, where an online parameter identification scheme is proposed to track the time-varying parameters of the process. An optimal guidance torque is calculated with respect to the level of interaction using the updated model. We validate the proposed approach by performing an experimental study with five participants in a guided lane, keeping task under different interaction behaviors of participants. The results show the system capability to adapt the control input based on the driver's acceptance on the torque intervention.

State-of-the-art autonomous cars use various algorithms for path planning in different environments. The design of these algorithms is difficult when the nonlinear and the nonholonomic aspect of the vehicle dynamics are dominant. These aspects are small at high speeds and for simple maneuvers at low speeds, so effective algorithms exist. However, path planning for more complex maneuvers at low speeds, especially in tight and cluttered environments, remains a difficult challenge. This paper proposes a new approach to this problem. The presented algorithm performs a tree-search on a discretized state space using dynamic programming. It is shown in simulation and experiments that even complicated paths can be computed very efficiently. Since a path is composed of a sequence of simple arcs, it is easy to track by a linear controller.

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 vehicle's 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.

We present a framework for autonomous driving which can learn from human demonstrations, and we apply it to the longitudinal control of an autonomous car. Offline, we model car-following strategies from a set of example driving sequences. Online, the model is used to compute accelerations which replicate what a human driver would do in the same situation. This reference acceleration is tracked by a predictive controller which enforces a set of comfort and safety constraints before applying the final acceleration. The controller is designed to be robust to the uncertainty in the predicted motion of the preceding vehicle. In addition, we estimate the confidence of the driver model predictions and use it in the cost function of the predictive controller. As a result, we can handle cases where the training data used to learn the driver model does not provide sufficient information about how a human driver would handle the current driving situation. The approach is validated using a combination of simulations and experiments on our autonomous vehicle.

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.

We propose a learning-based method for the longitudinal control of an autonomous vehicle on the highway. We use a driver model to generate acceleration inputs which are used as a reference by a model predictive controller. The driver model is trained using real driving data, so that it can reproduce the driver's behavior. We show the system's ability to reproduce different driving styles from different drivers. By solving a constrained optimization problem, the model predictive controller ensures that the control inputs applied to the vehicle satisfy some safety criteria. This is demonstrated on a vehicle by artificially creating potentially dangerous situations with virtual obstacles.

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.

All-way stop intersections are widely used for traffic management in North America. Therefore, modeling and control of vehicle behavior at stop intersections is fundamental for driver assistance systems and autonomous driving. This paper presents a method to predict the maneuvers performed by vehicles at arbitrary all-way stop intersections, using noisy sensor data. This is required for an autonomous vehicle to decide when to enter the intersection, or for a driver assistance system to decide when to issue a collision warning to the driver. The problem is divided into two components. The first component estimates the maneuver intention of the drivers by means of a naïve Bayesian filter. The second component predicts the order in which the vehicles will enter the intersection by means of a kinematic feedback model. Both algorithms are evaluated using real world data collected with laser sensors mounted on a vehicle. The Bayesian filter is successfully applied to intersections of different sizes and geometries. We show that the filter identifies maneuvers earlier than a deterministic reference model.

This paper proposes a novel algorithm to identify three inertial parameters: sprung mass, yaw moment of inertia, and longitudinal position of the center of gravity. A four-wheel nonlinear vehicle model with roll dynamics and a correlation between the inertial parameters is used for a dual unscented Kalman filter to simultaneously identify the inertial parameters and the vehicle state. A local observability analysis on the nonlinear vehicle model is used to activate and deactivate different modes of the proposed algorithm. Extensive CarSim simulations and experimental tests show the performance and robustness of the proposed approach on a flat road with a constant tire–road friction coefficient.

Threat assessment during semiautonomous driving is used to determine when correcting a driver's input is required. Since current semiautonomous systems perform threat assessment by predicting a vehicle's future state while treating the driver's input as a disturbance, autonomous controller intervention is limited to a restricted regime. Improving vehicle safety demands threat assessment that occurs over longer prediction horizons wherein a driver cannot be treated as a malicious agent. In this paper, we describe a real-time semiautonomous system that utilizes empirical observations of a driver's pose to inform an autonomous controller that corrects a driver's input when possible in a safe manner. We measure the performance of our system using several metrics that evaluate the informativeness of the prediction and the utility of the intervention procedure. A multisubject driving experiment illustrates the usefulness, with respect to these metrics, of incorporating the driver's pose while designing a semiautonomous system.

A robust control design is proposed for the lane-keeping and obstacle avoidance of semiautonomous ground vehicles. A robust Model Predictive Controller (MPC) is used in order to enforce safety constraints with minimal control intervention. An uncertain driver model is used to obtain sets of predicted vehicle trajectories in closed-loop with the predicted driver's behavior. The robust MPC computes the smallest corrective steering action needed to keep the driver safe for all predicted trajectories in the set. Simulations of a driver approaching multiple obstacles, with uncertainty obtained from measured data, show the effect of the proposed framework.

This paper presents the design of a novel active safety system preventing unintended roadway departures. The proposed framework unifies threat assessment, stability, and control of passenger vehicles into a single combined optimization problem. A nonlinear model predictive control (MPC) problem is formulated, where nonlinear vehicle dynamics, in closed-loop with a driver model, is used to optimize the steering and braking actions needed to keep the driver safe. A model of the driver's nominal behavior is estimated based on his observed behavior. The driver commands the vehicle, whereas the safety system corrects the driver's steering and braking actions in case there is a risk that the vehicle will unintentionally depart from the road. The resulting predictive controller is always active, and mode switching is not necessary. We show simulation results detailing the behavior of the proposed controller and experimental results obtained by implementing the proposed framework on embedded hardware in a passenger vehicle. The results demonstrate the capability of the proposed controller to detect and avoid roadway departures while avoiding unnecessary interventions.

In this paper we present a novel method for visual scanning and target tracking by means of independent pan-tilt cameras which mimic the chameleon visual system. We present a systematic and optimization-based approach to the problem, from the high-level to the low-level control. In particular, in the first part we develop a new algorithm for scanning the sphere using multiple cameras. The algorithm combines information about the environment and a model of target movement, to perform optimal scanning by means of stochastic dynamic programming. In the second part we develop a model-based control strategy for target tracking. A switching optimal control strategy based on smooth pursuit and saccades is designed by means of explicit model predictive control (MPC) theory. We simulated and experimentally validated our theory on a robotic chameleon head composed of two independent pan-tilt cameras. The resulting scanning pattern and target tracking has a remarkable resemblance to the one seen in nature by chameleons