## Dr. Andrea Carron
## Projects## Model Learning and Contextual Controller Tuning for Autonomous RacingModel predictive control has been widely used in the field of autonomous racing and many data-driven approaches have been proposed to improve the closed-loop performance and to minimize lap time. However, it is often overlooked that a change in the environmental conditions, e.g., when it starts raining, it is not only required to adapt the predictive model but also the controller parameters need to be adjusted. In this project, we address this challenge with the goal of requiring only few data. The key novelty of the proposed approach is that we leverage the learned dynamics model to encode the environmental condition as context. This insight allows us to employ contextual Bayesian optimization, thus accelerating the controller tuning problem when the environment changes and to transfer knowledge across different cars. The proposed framework is validated on an experimental platform with 1:28 scale RC race cars. We perform an extensive evaluation with more than 2’000 driven laps demonstrating that our approach successfully optimizes the lap time across different contexts faster compared to standard Bayesian optimization. ## A predictive safety filter for learning-based racing controlThe growing need for high-performance con- trollers in safety-critical applications like autonomous driving has been motivating the development of formal safety veri- fication techniques. In this project, we design and implement a predictive safety filter that is able to maintain vehicle safety with respect to track boundaries when paired alongside any potentially unsafe control signal, such as those found in learning-based methods. A model predictive control (MPC) framework is used to create a minimally invasive algorithm that certifies whether a desired control input is safe and can be applied to the vehicle, or that provides an alternate input to keep the vehicle in bounds. To this end, we provide a principled procedure to compute a safe and invariant set for nonlinear dynamic bicycle models using efficient convex approximation techniques. To fully support an aggressive racing performance without conservative safety interventions, the safe set is extended in real-time through predictive control backup trajectories. Applications for assisted manual driving and deep imitation learning on a miniature remote-controlled vehicle demonstrate the safety filter’s ability to ensure vehicle safety during aggressive maneuvers. ## Volume control of low-cost ventilator with automatic set-point adaptationThis project considers the control design for a low-cost ventilator that is based on a manual resuscitator bag (also known as AmbuBag) to pump air into the lungs of a patient who is physically unable to breathe. First, it experimentally shows that for accurately tracking tidal volumes, the controller needs to adjust to the individual patient and the different configurations, e.g., hardware or operation modes. Second, it proposes a set-point adaptation algorithm that uses sensor measurements of a flow meter to automatically adapt the controller to the setup at hand. Third, it shows in experiments on a mechanical lung simulator that such an adaptive solution improves the performance of the ventilator for various setups. One objective of this paper is to increase awareness of the need for feedback control using flow measurements in low-cost ventilator solutions in order to automatically adapt to the specific scenario. ## Low-cost Re-usable Electric Model RocketIn the last decade, autonomous vertical take- off and landing (VTOL) vehicles have become increasingly important as they lower mission costs thanks to their re- usability. However, their development is complex, rendering even the basic experimental validation of the required advanced guidance and control (G&C) algorithms prohibitively time- consuming and costly. In this project, we present the design of an inexpensive small-scale VTOL platform that can be built from off-the-shelf components for less than 1000 USD. The vehicle design mimics the first stage of a reusable launcher, making it a perfect test-bed for G&C algorithms. To control the vehicle during ascent and descent, we propose a real-time optimization-based G&C algorithm. The key features are a real-time minimum fuel and free-final-time optimal guidance combined with an offset-free tracking model predictive position controller. The vehicle hardware design and the G&C algo- rithm are experimentally validated both indoors and outdoor, showing reliable operation in a fully autonomous fashion with all computations done on-board and in real-time. ## Model predictive coverage controlCooperative robotic problems often require coordination in space in order to complete a given task, important examples include search and rescue, operations in hazardous environments, and autonomous taxi deployment. Events can be quickly detected by partitioning the working environment and assigning one robot to each partition. However, a crucial factor that limits the effectiveness and usage of coverage algorithms is related to the ability of taking decisions in the presence of constraints. In this paper, we propose a coverage control algorithm that is capable of handling nonlinear dynamics, and state and input constraints. The proposed algorithm is based on a nonlinear tracking model predictive controller and is proven to converge to a centroidal Voronoi configuration. We also introduce a procedure to design the terminal ingredients of the model predictive controller. The effectiveness of the algorithm is then highlighted with a numerical simulation. ## Collaborative Robotic Systems (Principal Investigator)The objective of this project is to unify distributed decision-making and robot control, studying algorithms that are capable of making optimal decisions while taking into account constraints such as the laws of motion, actuation limits and sensing capabilities of the robots. ## Learning-based Control for Robotic ArmsHigh-precision trajectory tracking is fundamental in robotic manipulation. While industrial robots address this through stiffness and high-performance hardware, compliant and cost-effective robots require advanced control to achieve accurate position tracking. In this project, we propose a model-based control approach, which makes use of data gathered during operation to improve the model of the robotic arm and thereby the tracking performance. The proposed scheme is based on an inverse dynamics feedback linearization and a data-driven error model, which are integrated into a model predictive control formulation. In particular, we show how offset-free tracking can be achieved by augmenting a nominal model with both a Gaussian process, which makes use of offline data, and an additive disturbance model suitable for efficient online estimation of the residual disturbance via an extended Kalman filter. The performance of the proposed offset-free GPMPC scheme is demonstrated on a compliant 6 degrees of freedom robotic arm, showing significant performance improvements compared to other robot control algorithms. ## Safe Learning for Distributed SystemsLearning in interacting dynamical systems can lead to instabilities and violations of critical safety constraints, which is limiting its application to constrained system networks. This work introduces two safety frameworks that can be applied together with any learning method for ensuring constraint satisfaction in a network of uncertain systems, which are coupled in the dynamics and in the state constraints. The proposed techniques make use of a safe set to modify control inputs that may compromise system safety, while accepting safe inputs from the learning procedure. Two different safe sets for distributed systems are proposed by extending recent results for structured invariant sets. The sets differ in their dynamical allocation to local sets and provide different trade-offs between required communication and achieved set size. The proposed algorithms are proven to keep the system in the safe set at all times and their effectiveness and behavior is illustrated in a numerical example. ## Probabilistic Invariant Sets for Linear SystemsDynamical systems with stochastic uncertainties are ubiquitous in the field of control, with linear systems under additive Gaussian disturbances a most prominent example. The concept of probabilistic invariance was introduced to extend the widely applied concept of invariance to this class of problems. Computational methods for their synthesis, however, are limited. In this work we present a relationship between probabilistic and robust invariant sets for linear systems, which enables the use of well-studied robust design methods. Conditions are shown, under which a robust invariant set, designed with a confidence region of the disturbance, results in a probabilistic invariant set. We furthermore show that this condition holds for common box and ellipsoidal confidence regions, generalizing and improving existing results for probabilistic invariant set computation. We finally exemplify the synthesis for an ellipsoidal probabilistic invariant set. Two numerical examples demonstrate the approach and the advantages to be gained from exploiting robust computations for probabilistic invariant sets. ## Scalable Model Predictive Control of Autonomous Mobility on Demand SystemsTechnological advances in self driving vehicles will soon enable the implementation of large-scale mobility-on-demand systems with autonomous agents. The efficient management of the vehicle fleet remains a key challenge, in particular for enabling a demand-aligned distribution of available vehicles, commonly referred to as rebalancing. In this work we present a discrete-time model of an autonomous mobility-on-demand system, in which unit capacity self driving vehicles serve transportation requests consisting of a (time, origin, destination) tuple on a directed graph. Time delays in the discrete time model are approximated as first-order lag elements yielding a sparse model suitable for model-predictive control. The well-posedness of the model is demonstrated and a characterization of its equilibrium points is given. Furthermore, we show the stabilizability of the model and propose a scalable model-predictive control scheme with complexity that scales linearly with the size of the city. We verify the performance of the scheme in a multi-agent transport simulation and demonstrate that service levels outperform those of existing rebalancing schemes at identical fleet sizes. ## Gaussian Process Regression via Kalman FilteringIn this project, we study the problem of efficient non-parametric estimation for non-linear time-space dynamic Gaussian processes (GP). We propose a systematic and explicit procedure to address this problem by pairing GP regression with Kalman Filtering. Under a specific separability assumption of the modeling kernel and periodic sampling on a (possibly non-uniform) space-grid, we show how to build an exact finite dimensional discrete-time state-space representation for the modeled process. The major finding is that the state at instant k of the associated Kalman Filter represents a sufficient statistic to compute the minimum variance prediction of the process at instant k over any arbitrary finite subset of the space. ## Coverage Control under Unknown Sensory FunctionsWe consider a scenario where the aim of a group of agents is to perform the optimal coverage of a region according to a sensory function. In particular, centroidal Voronoi partitions have to be computed. The difficulty of the task is that the sensory function is unknown and has to be reconstructed on line from noisy measurements. Hence, estimation and coverage needs to be performed at the same time. We cast the problem in a Bayesian regression framework, where the sensory function is seen as a Gaussian random field. Then, we design a set of control inputs which try to well balance coverage and estimation, also discussing convergence properties of the algorithm. ## Multi-agent Hitting TimeThis work provides generalized notions and analysis methods for the hitting time of random walks on graphs. The hitting time, also known as the Kemeny constant or the mean first passage time, of a random walk is widely studied; however, only limited work is available for the multiple random walker scenario. In this work we provide a novel method for calculating the hitting time for a single random walker as well as the first analytic expression for calculating the hitting time for multiple random walkers, which we denote as the group hitting time. We also provide a closed form solution for calculating the hitting time between specified nodes for both the single and multiple random walker cases. Our results allow for the multiple random walks to be different and, moreover, for the random walks to operate on different subgraphs. Finally, using sequential quadratic programming, we show that the combination of transition matrices that generate the minimal group hitting time for various graph topologies is often different. ## Relative Measurements ConsensusIn this proect, we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard least-squares problem, the main challenge is to devise scalable algorithms that allow each agent to estimate its own position by means of only local communication and bounded complexity, independently of the network size and topology. We propose a consensus-based algorithm with the use of local memory variables which allows asynchronous implementation, has guaranteed exponential convergence to the optimal solution under mild deterministic and randomised communication protocols, and requires minimal packet transmission. In the randomized scenario we then study the rate of convergence in expectation of the estimation error and we argue that it can be used to obtain upper and lower bound for the rate of converge in mean square. In particular, we show that for regular graphs the convergence rate in expectation is reduced by a factor N, which is the number of nodes, which is the same asymptotic degradation of memory-less asynchronous consensus algorithms. Additionally, we show that the asynchronous implementation is also robust to delays and communication failures. ## ARCADEThe Autonomous Rendezvous, Control And Docking Experiment (ARCADE) is a technology demonstrator aiming to prove automatic attitude determination and control, rendezvous and docking capabilities for small scale spacecraft and aircraft. The development of such capabilities could be fundamental to create, in the near future, fleets of cooperative, autonomous unmanned aerial vehicles for mapping, surveillance, inspection and remote observation of hazardous environments; small-class satellites could also benefit from the employment of docking systems to extend and reconfigure their mission profiles. ARCADE is designed to test these technologies on a stratospheric flight on board the BEXUS-17 balloon, allowing to demonstrate them in a harsh environment subjected to gusty winds and high pressure and temperature variations. ## Cooperative and Competitive Receding Horizon Control AlgorithmsWe consider the problem of controlling two dynamically decoupled agents which can cooperate or compete. Agents are modelled as linear discrete time systems, and collect each other’s state information without delays. Control actions are computed using a Receding Horizon framework, where each agent’s controllers are computed by minimizing a linear, quadratic cost function which depends on both agents’ states. Cooperation or competition is specified throught the state tracking objectives of each agent. We do not consider state constraints. The simplicity of our framework allows us to provide the following results analytically: 1) When agents compete, their states converge to an equilibrium trajectory where the steady state tracking error is finite. 2) Limit-cycles cannot occur. Numerical simulations and experiments done with a LEGO Mindstorm multiagent platform match our analytical results. } { |