In this project, we study a scalable mechanism for designing scalable control algorithms for large-scale safety-critical multi-robot systems (MRS). We started with a distributed graph-based Control Barrier Function formulation, termed GCBF, for encoding the safety requirements in MRS. The results were published in these CoRL'23 and IEEE TRO'25 papers. We proposed a learning-based architecture to find GCBF for MRS modeled under general nonlinear control affine dynamics. In particular, we utilize Graph Neural Networks (GNNs) to encode the relative state information (through edge features) and the type of neighbors, i.e., another controlled agent, a stationary obstacle, or a moving obstacle (through node features). More details on these results can be found here on the project website.  

The next challenge with MRS is when the robots are exploring unknown territories and require inter-agent connections to maintain communication with each other and share the individually acquired knowledge to build collective team intelligence. When such an MRS traverses an obstacle field, this connectivity requirement leads to deadlock situations for the MRS where even one of the robots getting stuck in a deadlock leads to the deadlock of the whole MRS. To tackle this problem, we proposed a hierarchical control architecture where a high-level planner intervenes upon detection of deadlocks and issues commands to assist with deadlock resolution. The results were published in IEEEDC'24.  

The specific high-planner we designed in this work assigns a leader and a set of waypoints for the leader upon deadlock detection through a heuristic. In this case, the challenge is how to scale this heuristic high-level planner for large-scale MRS so that it does not lead to conservative behaviors. For systematic leader and waypoint assignments, we explored foundation models as the high-level planners in our more recent project. This is an ongoing project, and we are exploring the optimal way to utilize a variety of foundation models, such as text-based LLMs and multi-modal VLMs, as high-level planners for this complex problem. 

Fault-tolerant control design using neural fault predictor

A sudden actuator fault in a safety-critical system can cause safety violations and severe consequences. Existing fault-tolerant control (FTC) approaches normally focus on maintaining system performance and do not consider system safety. Furthermore, most of the existing approaches require accurate knowledge of the system model for fault detection and isolation (FDI). This work explores a model-free approach for fault detection, utilizing the system input-output data instead of the state information.  The proposed approach is not required to either learn the system model or create a reduced-order representation of the model. Instead, we use the system output and the commanded input as the features of a neural network, which directly predicts whether there is an actuator fault. Our initial results have been published in this paper. This work's current focus is associating either a deterministic or a probabilistic guarantee on the correctness of the neural fault detector, or in other words, deterministic or probabilistic bounds of false negatives. 

Quadratic program-based safe control design

Driving the state of a dynamical system to a given desired point or a desired set in the presence of constraints is a problem of major practical importance. Constraints requiring the system trajectories to evolve in some safe set at all times while visiting some goal set(s) are common in safety-critical applications. Constraints on convergence to a goal set within a fixed time often appear in time-critical applications, e.g., when a task must be completed within a given time interval. Spatiotemporal specifications impose spatial (state) as well as temporal (time) constraints on the system trajectories. This work presents a control synthesis framework for a general class of nonlinear, control-affine systems under spatiotemporal and input constraints. We considered the problem of finding a control input that confines the closed-loop system trajectories in a safe set and steers them to a goal set within a fixed time. To this end, we presented a Quadratic Programming (QP) formulation to compute the corresponding control input. We use slack variables to guarantee the feasibility of the proposed QP under input constraints. Furthermore, when strict complementary slackness holds, we showed that the solution of the QP is a continuous function of the system states and established the uniqueness of closed-loop solutions to guarantee forward invariance using Nagumo’s theorem. Our results were published in this Automatica'22 paper. 

Fixed-time gradient flows

Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for achieving acceleration, based on the recently introduced notion of fixed-time stability of dynamical systems. The method presents itself as a generalization of simple gradient-based methods suitably scaled to achieve convergence to the optimizer in a fixed time, independent of the initialization. We achieve this by first leveraging a continuous-time framework for designing fixed-time stable dynamical systems and later providing a consistent discretization strategy such that the equivalent discrete-time algorithm tracks the optimizer in a practically fixed number of iterations. We validate the accelerated convergence properties of the proposed schemes on a range of numerical examples against state-of-the-art optimization algorithms. Our work provides insights into developing novel optimization algorithms by discretizing continuous-time flows. This work has been published in several papers (IEEE TAC'21, IEEE TAC'23, AAAI'22).