Dwaipayan Mukherjee

Dwaipayan Mukherjee, Shashi Ranjan Kumar

This paper presents a finite-time heterogeneous cyclic pursuit scheme that ensures consensus among agents modelled as integrators. It is shown that for the proposed sliding mode control, even when the gains corresponding to each agent are non-identical, consensus results within a finite-time provided all the gains are positive. An algorithm is presented to compute the consensus value and consensus time for a given set of gains and initial states of the agents. The set of values where consensus can occur, by varying the gains, has been derived and a second algorithm aids in determining the gains that enable consensus at any point in the aforementioned set, within a given finite-time. As an application, the finite-time consensus in line-of-sight (LOS) rates, over a cycle digraph, for a group of interceptors is shown to be effective in ensuring co-operative collision-free interception of a target, for both kinematic and realistic models of the interceptors. Simulations vindicate the theoretical results.

Abhinav Sinha, Shashi Ranjan Kumar, Dwaipayan Mukherjee

This paper considers a pursuit-evasion scenario among three agents -- an evader, a pursuer, and a defender. We design cooperative guidance laws for the evader and the defender team to safeguard the evader from an attacking pursuer. Unlike differential games, optimal control formulations, and other heuristic methods, we propose a novel perspective on designing effective nonlinear feedback control laws for the evader-defender team using a time-constrained guidance approach. The evader lures the pursuer on the collision course by offering itself as bait. At the same time, the defender protects the evader from the pursuer by exercising control over the engagement duration. Depending on the nature of the mission, the defender may choose to take an aggressive or defensive stance. Such consideration widens the applicability of the proposed methods in various three-agent motion planning scenarios such as aircraft defense, asset guarding, search and rescue, surveillance, and secure transportation. We use a fixed-time sliding mode control strategy to design the control laws for the evader-defender team and a nonlinear finite-time disturbance observer to estimate the pursuer's maneuver. Finally, we present simulations to demonstrate favorable performance under various engagement geometries, thus vindicating the efficacy of the proposed designs.

Dwaipayan Mukherjee, Daniel Zelazo

The present paper investigates the robustness of the consensus protocol over weighted directed graphs using the Nyquist criterion. The limit to which a single weight can vary, while consensus among the agents can be achieved, is explicitly derived. It is shown that even with a negative weight on one of the edges, consensus may be achieved. The result obtained in this paper is applied to a directed acyclic graph and to the directed cycle graph. Graph theoretic interpretations of the limits are provided for the two cases. Simulations support the theoretical results.