Joel G. Manathara

Bio: Joel G. Manathara is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Acceleration & Search algorithm. The author has an hindex of 4, co-authored 6 publications receiving 40 citations.

Cooperative Multiple Pursuers against a Single Evader

Abstract: This paper considers a pursuit-evasion game for non-holonomic systems where a group of pursuers attempts to capture an evader in a bounded connected domain. The problem is challenging because all vehicles have the same maneuvering capability in terms of speed and turn radius constraint. The paper initially discusses a simple approach for holonomic systems that is based on the minimization of the safe-reachable area (the area containing the set of points to where an evader can travel without being caught). This idea is then extended to develop a pursuit-evasion strategy for non-holonomic systems. However, solving such a problem is computationally intractable. Therefore, we propose a computationally efficient algorithm to obtain approximate solutions. This paper also proposes an alternative approach to obtain a simple yet effective solution to the cooperative pursuit problem that is based on missile guidance laws. As there is no analytical proof of capture, we empirically evaluate the performance of the algorithms and perform a comparative study using solutions obtained from umpteen simulations. A total of four different cooperative pursuit strategies and three different evader strategies are taken into account for the comparative study. In the process, an evader strategy which is superior to that based on the optimization of safe-reachable area is also identified.

A cooperative pursuit-evasion game for non-holonomic systems

Abstract: -This paper considers a pursuit-evasion game for non-holonomic systems where a number of pursuers attempt to capture a single evader in a bounded connected domain. The problem is challenging because all vehicles have the same manoeuvring capability and are subject to turn radius constraints making them non-holonomic systems. The paper initially presents simple and alternate proofs for results existing in the literature that guarantee capture for holonomic systems. These results that are based on the minimization of safe-reachable area (the set of points where an evader can travel without being caught) are then extended to non-holonomic systems. However, solving such a problem exactly is computationally intractable. Therefore, the paper proposes a computationally efficient algorithm to obtain an approximate solution to the safe-reachable area minimization problem where the pursuers aim to minimize the safe-reachable area of the evader, while the evader chooses control actions to maximize it. Also proposed is an alternative approach that uses a cooperative strategy based on a pure proportional navigation law to capture the evader. In the process, an evader strategy which is superior to those based on the minimization of safe-reachable area is identified. The paper evaluates the proposed algorithms through numerical simulations.

NMPC Based Approach for Cooperative Target Defence

Abstract: We consider a three-agent pursuit-evasion problem involving an attacker, and a target-defender team. The goal of the attacker is to capture the target, while that of the target is to escape the capture and the goal of the defender is to intercept the attacker before the attacker reaches the target. The defender and the target cooperate such that their objective is achieved efficiently. The target-defender team do not have accurate information of the attacker and hence use Extended Kalman Filter to estimate its states. The target-defender team uses Nonlinear Model Predictive Control (NMPC) to compute their optimal control inputs, while the attacker switches between pure pursuit and proportional navigation guidance laws about which the team is unaware of. The performance of the solution obtained from the proposed NMPC formulation was evaluated through numerical simulations and hardware experiments performed using ground rovers.

Acceleration control of a multi-rotor UAV towards achieving microgravity

Abstract: In this paper, we present control and parameter estimation strategies with theoretical guarantees to turn a hex-rotor unmanned aerial vehicle (UAV) into a microgravity enabling platform. We make the UAV to maintain a constant acceleration equal to free-fall acceleration for it and any payload on-board to experience microgravity. Towards this, we derive a feedback linearisation-based acceleration control law exploiting the differential flatness property of our system. The proposed control law requires the estimates of the system parameters. Therefore, ancillary to this control law, we propose a parameter estimation scheme and prove that the proposed control law along with the parameter estimation scheme ensures convergence of acceleration to the desired value under certain conditions. We also characterize these conditions that guarantee convergence. The flight tests that we have performed employing the proposed control and parameter estimation schemes gave microgravity levels of the order of $$10^{-3}g$$ for 1.6 s. To our knowledge, our hex-rotor UAV is the first multi-rotor UAV to achieve microgravity, and the first UAV—fixed-wing or rotary—to attain and maintain such levels of microgravity.

Multi-Target Motion Planning Amidst Obstacles for Autonomous Aerial and Ground Vehicles

Abstract: The motion planning problem of a single autonomous vehicle having a minimum turn radius constraint, visiting an ordered sequence of targets in an environment with polygonal obstacles, is addressed. Two types of vehicles are considered: aerial/ground vehicle - described by the Dubins/Reeds-Shepp vehicle models, respectively. The problem is posed in the form of a search tree by using the obstacles’ vertices, vehicle’s initial configuration, and the set of target points as nodes. The tree’s arcs are represented by the Dubins/Reed-Shepp paths without terminal angle constraint (relaxed paths) connecting two adjacent nodes. These relaxed paths - connecting an initial configuration and a destination, are calculated using a feedback algorithm. Due to the computational complexity of the problem a genetic algorithm is proposed. Additionally, two deterministic search algorithms are presented. A quick heuristic greedy algorithm which uses the visibility graph distances for estimating the remaining vehicle path and an exhaustive algorithm which provides optimal solution trajectories. The performance of the algorithms is demonstrated and compared through sample runs and a Monte Carlo study. Results confirm that the heuristic algorithm provides relatively good solution for a small radius turn vehicle, while the genetic algorithm offers a good trade-off between computational load and performance.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Intercepting Rogue Robots: An Algorithm for Capturing Multiple Evaders With Multiple Pursuers

Abstract: We propose a distributed algorithm for the cooperative pursuit of multiple evaders using multiple pursuers in a bounded convex environment. The algorithm is suitable for intercepting rogue drones in protected airspace, among other applications. The pursuers do not know the evaders' policy, but by using a global “area-minimization” strategy based on a Voronoi tessellation of the environment, we guarantee the capture of all evaders in finite time. We present a decentralized version of this policy applicable in two-dimensional (2-D) and 3-D environments, and show in multiple simulations that it outperforms other decentralized multipursuer heuristics. Experiments with both autonomous and human-controlled robots were conducted to demonstrate the practicality of the approach. Specifically, human-controlled evaders are not able to avoid capture with the algorithm.

Reach-Avoid Games With Two Defenders and One Attacker: An Analytical Approach

Abstract: This paper considers a reach-avoid game on a rectangular domain with two defenders and one attacker. The attacker aims to reach a specified edge of the game domain boundary, while the defenders strive to prevent that by capturing the attacker. First, we are concerned with the barrier, which is the boundary of the reach-avoid set, splitting the state space into two disjoint parts: 1) defender dominance region (DDR) and 2) attacker dominance region (ADR). For the initial states lying in the DDR, there exists a strategy for the defenders to intercept the attacker regardless of the attacker’s best effort, while for the initial states lying in the ADR, the attacker can always find a successful attack strategy. We propose an attack region method to construct the barrier analytically by employing Voronoi diagram and Apollonius circle for two kinds of speed ratios. Then, by taking practical payoff functions into considerations, we present optimal strategies for the players when their initial states lie in their winning regions, and show that the ADR is divided into several parts corresponding to different strategies for the players. Numerical approaches, which suffer from inherent inaccuracy, have already been utilized for multiplayer reach-avoid games, but computational complexity complicates solving such games and consequently hinders efficient on-line applications. However, this method can obtain the exact formulation of the barrier and is applicable for real-time updates.

Pursuit-Evasion Games of High Speed Evader

Abstract: In this paper, we address pursuit-evasion games of high speed evader involving multiple pursuers and a single evader with holonomic constraints in an open domain. The existing work on this problem discussed the required formation and capture strategy for a group of pursuers. However, the formulation has mathematical errors and has raised concerns over the validity of the developed capture strategy. This paper uses the idea of Apollonius circle to develop an escape strategy for the high speed evader, resolving the shortfalls in the existing work. The strategy is built on a concept of perfectly encircled formation and the conditions required to construct the same are presented. The escape strategy contains two steps. Firstly, the evader employs a strategy that forces a gap in the formation against all the admissible strategies of a group of pursuers. In the second step, it uses this gap to escape. The strategy considers both direct and indirect gaps in the formations. The indirect gap is encountered when a group of three or four pursuers is employed to capture. The efficacy of the escape strategy is established using simulation results.

A Decentralized Fuzzy Learning Algorithm for Pursuit-Evasion Differential Games with Superior Evaders

Abstract: In this paper, we consider multi-pursuer single-superior-evader pursuit-evasion differential games where the evader has a speed that is similar to or higher than the speed of each pursuer. A new fuzzy reinforcement learning algorithm is proposed in this work. The proposed algorithm uses the well-known Apollonius circle mechanism to define the capture region of the learning pursuer based on its location and the location of the superior evader. The proposed algorithm uses the Apollonius circle with a developed formation control approach in the tuning mechanism of the fuzzy logic controller (FLC) of the learning pursuer so that one or some of the learning pursuers can capture the superior evader. The formation control mechanism used by the proposed algorithm guarantees that the pursuers are distributed around the superior evader in order to avoid collision between pursuers. The formation control mechanism used by the proposed algorithm also makes the Apollonius circles of each two adjacent pursuers intersect or be at least tangent to each other so that the capture of the superior evader can occur. The proposed algorithm is a decentralized algorithm as no communication among the pursuers is required. The only information the proposed algorithm requires is the position and the speed of the superior evader. The proposed algorithm is used to learn different multi-pursuer single-superior-evader pursuit-evasion differential games. The simulation results show the effectiveness of the proposed algorithm.