## Pesticide Scheduling and Precision Agriculture

Collaborators: Usman Ali and Magnus Egerstedt

Agricultural automation presents challenges typically encountered in the realm of cyber-physical systems, such as incomplete information (plant health indicators), external disturbances (weather), limited control authority (fertilizers cannot make a plant mature arbitrarily fast), and a combination of discrete events and continuous plant dynamics. In this project, we focus on the particular problem of optimal pesticide spray scheduling. In particular, we look at pesticide application in blueberries, a crop of increasing economic relevance in the state of Georgia. Regulations impose strict requirements on scheduling, e.g., individual pesticides are only effective during certain seasons and pesticides cannot be sprayed too close to harvest time. We have shown how to translate these requirements to a temporal logic formula over the space of possible schedules. We then use the theory of optimal mode scheduling to generate a schedule that minimizes the risk of various infestations over time while guaranteeing the satisfaction of the constraints. Current research includes incorporating expert-derived models of disease propagation and weather forecasting into the scheduling algorithm.

## Provably Safe Adaptive Cruise Control

Collaborators: Thomas Waters, Xiangru Xu, and Aaron Ames

Adaptive cruise control (ACC) is the automated speed regulation of a vehicle to ensure that it maintains a safe time headway (ratio of distance to speed) with respect to the vehicle in front of it. We build on previous work using control barrier functions (CBFs), which provide a necessary condition for a controller to render a set forward invariant, to accomplish this. We study the particular scenario in which a car traveling in a parallel lane may elect to change lanes in between the controlled car and the lead car. We model this scenario as a hybrid system with modes corresponding to whether a car is present in an adjacent lane. A naive extension of the CBF approach does not work for the multiple car scenario and we therefor provide necessary conditions for forward invariance of hybrid systems executions with dwell time constraints. As a byproduct, we developed the notion of a time-varying CBF, which certifies forward invariance of time-indexed safe sets. Currently, we are evaluating our results using CarSim and expanding the class of problems we can address using this approach.

## Provably Correct Coordination of Multi-Robot Teams

Collaborators: Yancy Diaz-Mercado, Magnus Egerstedt, and Calin Belta

This work addresses how to control a team of robots with different capabilities to accomplish high-level interaction (coordination, sensing, and communication) missions. We have defined a novel specification language, called Braid Temporal Logic (BTL), that allows us to specify rich, temporally-layered tasks involving agents’locations in an environment, their relative positions to each other, and frequency of location swaps and information exchanges between agents. An example of such a task is ” The distance between agents 2 and 3 is never greater than 200 m. At least two different agents survey location 4. If agent 1 communicates with agent 2, then agent 2 passes the message to agent 4 or 5.”. By combining techniques from computer science and control theory, we are able to synthesize controllers for a given team of agent that is guaranteed to accomplish the mission and avoid inter-agent collisions. We have implemented our techniques on wheeled robots in the lab.

## Learning to Enforce Rich Specifications

Collaborators: Derya Aksaray, Zhaodan Kong, and Calin Belta

This work addresses the problem of steering a system with unknown, stochastic dynamics to satisfy a rich, temporally-layered task given as a temporal logic formula. We have developed provably convergent reinforcement learning algorithms to maximize the probability of satisfying a given formula and to maximize the average expected robustness, i.e., a measure of how strongly the formula is satisfied. We have demonstrated in simulation that reinforcement learning with robustness maximization performs better than probability maximization in terms of both probability of satisfaction and expected robustness. Current research directions include applying our method to higher-dimensional systems and adapting our reinforcement learning algorithms to operate over continuously-valued decision variables.

## Learning Patterns of Cyber-Physical Systems

Collaborators: Zhaodan Kong, Iman Haghighi, Ebru Aydin-Gol, Ana Medina Ayala, Igor Cizelj, Radu Grosu, Ezio Bartocci, and Calin Belta

Increased complexity of modern systems necessitates automated anomaly detection methods to detect possible anomalous behavior determined by malfunctions or external attacks. In this project, we focus on learning high-level descriptions of a system’s behavior by analyzing execution data and use this to diagnose security breaches or faults. We have developed formal methods for inferring (via supervised learning) and detecting (via unsupervised learning) anomalous behavior. Our procedures use data to construct temporal logic (TL) formulas that describes normal system behavior. This logic can be used to formulate properties such as “If the train brakes within 500 m of the platform at a speed of 50 km/hr, then it will stop in at least 30 s and at most 50 s.” Our procedure infers not only the physical parameters involved in the formula (e.g., 500 m in the example above) but also its logical structure. Temporal logic gives a more human-readable representation of behavior than classifiers represented as surfaces in high-dimensional feature spaces. Our methods have been applied to gene networks, naval surveillance, and power systems . Current research directions include expanding the kinds of properties we can learn and learning formulas for multiple classes of normal and anomalous behavior.

## Information Gathering under Constraints

Collaborators: Kevin Leahy, Mac Schwager, and Calin Belta

In this project, we address the problem of controlling a robot with known dynamics to gather the maximum amount of information about some unknown feature while still satisfying high-level constraints on its motion given as a temporal logic formula. An example of this kind of problem is steering a robot on the surface of Mars to ensure that it collects as much scientifically-relevant information about soil while also avoiding hard-to-traverse terrain, ensuring that it visits locations where it will have a good link with the ground crew, and visiting locations where it can gather enough sunlight. This problem is challenging because each action the robot takes affects which parts of the environment its sensors can cover and its progress towards satisfying the given specification. To solve this problem, we have developed algorithms that combine computer science with discrete optimization. Our algorithms are guaranteed to obey constraints and have been shown in simulation and experimentally to out-perform a base-line approach. We have considered finite-time, infinite-time, and multi-robot versions of this problem. Current research includes further experimental validation and gathering information with multiple sensing modalities.

## Decision-Making under Uncertainty

Collaborators: Kevin Leahy, Cristian Ioan-Vasile, Eric , Mac Schwager, and Calin Belta

This research project addresses accomplishing complex tasks under pervasive uncertainty about the environment in which a system operates. An example of such a problem is steering a robot to find survivors after a natural disaster and guide any found survivors to a safe location. We have developed a new temporal logic, called distribution temporal logic, that is capable of reasoning about the time evolution of not only the state of the system but also the uncertainty in this state. An example of a property that can be expressed in DTL is “Ensure that the uncertainty about the locations of fires remains below U for all time. If a survivor is found with probability P, guide the survivor to a safe location.” We have developed a verification algorithm that computes with what probability a given execution of a system satisfies a given specification. This can be used as a tool for algorithm evaluation. Currently, we are working to overcome the “curse of dimensionality” inherent in this problem by defining a specification language over Gaussian distributions. We are combining this with computer science and sample-based path planning techniques to develop a computationally feasible technique for robotic navigation under uncertainty and complex specifications.