Optimal Intermittent Sensing for Pursuit-Evasion Games

We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is a remote sensor (e.g., a radar station) that can sense the evader's location upon a request from the pursuer and communicate that sensed location to the pursuer. The pursuer has a budget on the total number of sensing requests. The outcome of the game is determined by the sensing and motion strategies of the players. We obtain an equilibrium sensing strategy for the pursuer and an equilibrium motion strategy for the evader. We quantify the degradation in the pursuer's pay-off due to its sensing limitations

Efficient Communication for Pursuit-Evasion Games with Asymmetric Information

We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is an immobile sensor (e.g., a ground radar station) that can sense the evader's location and communicate that information intermittently to the pursuer. Transmitting the information from the sensor to the pursuer is costly and only a finite number of transmissions can happen throughout the entire game. The outcome of the game is determined by the control strategies of the players and the communication strategy between the sensor and the pursuer. We obtain the (Nash) equilibrium control strategies for both the players as well as the optimal communication strategy between the static sensor and the pursuer. We discuss a dilemma for the evader that emerges in this game. We also discuss the emergence of implicit communication where the absence of communication from the sensor can also convey some actionable information to the pursuer

Timed Automata Approach for Motion Planning Using Metric Interval Temporal Logic

In this paper, we consider the robot motion (or task) planning problem under some given time bounded high level specifications. We use metric interval temporal logic (MITL), a member of the temporal logic family, to represent the task specification and then we provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find a feasible motion (or path) sequence for the robot to complete the task.Comment: Full Version for ECC 201

Target Defense against Periodically Arriving Intruders

We consider a variant of pursuit-evasion games where a single defender is tasked to defend a static target from a sequence of periodically arriving intruders. The intruders' objective is to breach the boundary of a circular target without being captured and the defender's objective is to capture as many intruders as possible. At the beginning of each period, a new intruder appears at a random location on the perimeter of a fixed circle surrounding the target and moves radially towards the target center to breach the target. The intruders are slower in speed compared to the defender and they have their own sensing footprint through which they can perfectly detect the defender if it is within their sensing range. Considering the speed and sensing limitations of the agents, we analyze the entire game by dividing it into partial information and full information phases. We address the defender's capturability using the notions of engagement surface and capture circle. We develop and analyze three efficient strategies for the defender and derive a lower bound on the capture fraction. Finally, we conduct a series of simulations and numerical experiments to compare and contrast the three proposed approaches.Comment: To be presented at the 2023 American Control Conference - May 31 - June 2, 2023, in San Diego, CA, US

CONTROLLER SYNTHESIS UNDER INFORMATION AND FINITE-TIME LOGICAL CONSTRAINTS

In robotics, networks, and many related fields, a typical controller design problem needs to address both logical and informational constraints. The logical constraints may arise due to the complex task description or decision making process, while the information-related constraints emerge naturally as a consequence of the limitations on communication and computation capabilities. In the first part of the thesis, we consider the problem of synthesizing an event-based controller to address the information-related constraints in the controller design. We consider dynamical systems that are operating under continuous state feedback. This assumes that the measurements are continuously transmitted to the controller in order to generate the input and thus, increases the cost of communication by requiring huge communication resources. In many situations, it so happens that the measurement does not change fast enough that continuous transmission is required. Taking motivation from this, we consider the case where instead continuous feedback we seek an intermittent-feedback. As a result, the system trajectory will deviate from its ideal behavior. However, the question is how much would it deviate? Given the allowed bound on this deviation, can we design some controller that requires fewer measurements than the original controller and still manages to keep the deviation within this prescribed bound? Two important questions remain: 1) What will be the structure of the (optimal) controller? 2) How will the system know the (optimal) instances to transmit the measurement? When the system sends out measurement to controller, it is called as an ``event". Thus, we are looking for an event-generator and a controller to perform event-based control under the constraints on the availability of the state information. The next part focuses on controller synthesis problems that have logical, spatio-temporal constraints on the trajectory of the system; a robot motion planning problem fits as a good example of these kind of finite-time logically constrained problems. We adopt an automata-based approach to abstract the motion of the robot into an automata, and verify the satisfaction of the logical constraints on this automata. The abstraction of the dynamics of the robot into an automata is based on certain reachability guarantee of the robot's dynamics. The controller synthesis problem over the abstracted automata can be represented as a shortest-path-problem. In part III, we consider the problem of jointly addressing the logical and information constraints. The problem is approached with the notion of robustness of logical constraints. We propose two different frameworks for this problem with two different notions of robustness and two different approaches for the controller synthesis. One framework relies on the abstraction of the dynamical systems into a finite transition system, whereas the other relies on tools and results from prescribed performance control to design continuous feedback control to satisfy the robust logical constraints. We adopt an hierarchical controller synthesis method where a continuous feedback controller is designed to satisfy the (robust) logical constraints, and later, that controller is replaced by a suitable event-triggered intermittent feedback controller to cope with informational constraints

Communication-Aware Map Compression for Online Path-Planning

This paper addresses the problem of the communication of optimally compressed information for mobile robot path-planning. In this context, mobile robots compress their current local maps to assist another robot in reaching a target in an unknown environment. We propose a framework that sequentially selects the optimal compression, guided by the robot's path, by balancing the map resolution and communication cost. Our approach is tractable in close-to-real scenarios and does not necessitate prior environment knowledge. We design a novel decoder that leverages compressed information to estimate the unknown environment via convex optimization with linear constraints and an encoder that utilizes the decoder to select the optimal compression. Numerical simulations are conducted in a large close-to-real map and a maze map and compared with two alternative approaches. The results confirm the effectiveness of our framework in assisting the robot reach its target by reducing transmitted information, on average, by approximately 50% while maintaining satisfactory performance