Currently, I am interested in two primary research areas: Multiplayer Reach-Avoid Differential Games; and Feedback Control of Underactuated Systems.
Multiplayer reach-avoid games model strategic interactions, where a team of evaders aims to reach a target while avoiding an adversarial team of pursuers. Such interactions arise in various real-world scenarios, including safe motion/path planning, region protection in the presence of hostile agents, and dynamic collision avoidance.
Differential game theory provides a mathematical framework for modeling and analyzing multiplayer reach-avoid games. The standard approach to solving a reach-avoid differential game (RADG) begins with addressing the fundamental question of which team succeeds from a given initial state. This phase, known as the Game of Kind, divides the state space into regions where either pursuers or evaders emerge victorious. Subsequently, the Game of Degree is focused on identifying optimal strategies for all agents in state feedback format. Accomplishing this entails solving the intricate Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE).
In particular, my research on multiplayer reach-avoid differential games includes the following two problems:
Optimal Role Assignment for Multiplayer Reach-Avoid Differential Games in 3D Space - In this work, a multiplayer RADG with n pursuers and m evaders is studied. Using the analytical solution to the simpler case with n=m=1, an assignment scheme of pursuers to evaders is designed that allows the analytical solution to the mutliplayer game. A preliminary version of the draft can be found at https://doi.org/10.48550/arXiv.2303.07885.
Optimal Strategies for Single Pursuer vs Multiple Evaders in Reach-Avoid Games - In this work, an RADG with 1 pursuer and n cooperating evaders is considered. The optimal strategies for the evaders are shown to be identical to an RADG with n=1, which can be obtained by analytically solving the simple case of 1 pursuer 1 evader. Then, an alternate framework is proposed to obtain the optimal strategy of the pursuer.
Safety and Reachability in Reach-Avoid Games - Many practical scenarios where agents must reach designated goal states while avoiding restricted regions can be naturally formulated as RADGs. We are currently investigating such problems, with a particular focus on incorporating reinforcement learning as a tool to approximate solutions in settings where analytical characterizations are intractable.
Optimal Scheduling for Sequential Capture in Reach-Avoid Games - This work studies an RADG with one pursuer and multiple cooperating evaders under the assumption that the pursuer captures evaders in a sequential manner. A neural network-based function approximator is employed to estimate the Value function of the game, enabling the design of effective scheduling strategies for the pursuer.
Several systems in practical scenarios often have lesser number of actuators than the desired degree of freedom for the system. Control design of such underactuated systems is of critical importance in engineering literature.
In particular, my research on feedback control of underactuated systems includes the following two problems:
Trajectory Tracking and Stabilization of Sensor LOS in an Inertially Stabilized Platform - Precisely controlling the line-of-sight (LOS) orientiation of an optical sensor mounted on mobile platform is crucial. Here, a feedback control law was designed to obtain desired trajectory tracking and stabilization of the sensor LOS. This work was presented at the European Control Conference 2024 (link).
Trajectory Tracking of an AUV - A typical autonomous underwater vehicle (AUV) allows for 6 degrees of freedom. To aid in analysis, the dynamics of an AUV is often decomposed into weakly interacting models for lateral and vertical motion. In this work, we propose a feedback controller for desired trajectory tracking of the lateral motion model.
I worked with my guide Dr. Bharath Bhikkaji in collaboration with BigCat Wireless to implement a two-axis inertially stabilized platform (ISP). During this period I studied the mechanics of rotating systems and a multi-axis gimbal system in particular. After gaining a solid understanding of the theory, I modeled and stabilized a two-axis ISP on Simulink platform using a robust PID controller that could track any given reference signal with 0.1 degree RMS error at steady state. Finally, I proposed a feedback linearization based control law for the two-axis gimbal system.
I worked under the supervision of Dr. Dipti Patra for the fulfillment of my undergraduate thesis. I did a comprehensive study of the various kinds of super-resolution methods. To gain groundwork on the topic, I implemented all the basic interpolation-based techniques in Python. Then, I studied the various metrics to measure the similarity of image patches and did a comparative study of the performance of these different metrics in a Markov network-based super-resolution algorithm. Finally, I implemented a CNN-based super-resolution algorithm on MATLAB that was used to enhance the image quality obtained from a security camera.