Mangal Kothari

Chance Constrained RRT for Probabilistic Robustness to Environmental Uncertainty

between planner conservatism and the risk of infeasibility. This paper presents a novel real-time planning algorithm, chance constrained rapidly-exploring random trees (CC-RRT), which uses chance constraints to guarantee probabilistic feasibility for linear systems subject to process noise and/or uncertain, possibly dynamic obstacles. By using RRT, the algorithm enjoys the computational benets of sampling-based algorithms, such as trajectory-wise constraint checking and incorporation of heuristics, while explicitly incorporating uncertainty within the formulation. Under the assumption of Gaussian noise, probabilistic feasibility at each time step can be established through simple simulation of the state conditional mean and the evaluation of linear constraints. Alternatively, a small amount of additional computation can be used to explicitly compute a less conservative probability bound at each time step. Simulation results show that this algorithm can be used for ecient identication and execution of probabilistically safe paths in real time.

Cooperative target-capturing with inaccurate target information

This paper presents a distributed target-centric formation control strategy for multiple unmanned aerial vehicles (UAVs) in the presence of target motion uncertainty. The formation is maintained around a target using a combination of a consensus protocol and a sliding mode control law. Consensus helps in distributing the target information which is available only to a subset of vehicles. Sliding mode control compensates for the uncertainty in the target information. Hence, collectively the combined strategy enforces each of the vehicles to maintain its respective position in the formation. We show that if at least one vehicle in a group has target information with some uncertainty and the corresponding communication graph is connected, then a target-centric formation can be maintained. The performance of the proposed strategy is illustrated through simulations.

A Probabilistically Robust Path Planning Algorithm for UAVs Using Rapidly-Exploring Random Trees

The computationally efficient search for robust feasible paths for unmanned aerial vehicles (UAVs) in the presence of uncertainty is a challenging and interesting area of research. In uncertain environments, a “conservative” planner may be required but then there may be no feasible solution. In this paper, we use a chance constraint to limit the probability of constraint violation and extend this framework to handle uncertain dynamic obstacles. The approach requires the satisfaction of probabilistic constraints at each time step in order to guarantee probabilistic feasibility. The rapidly-exploring random tree (RRT) algorithm, which enjoys the computational benefits of a sampling-based algorithm, is used to develop a real-time probabilistically robust path planner. It incorporates the chance constraint framework to account for uncertainty within the formulation and includes a number of heuristics to improve the algorithm’s performance. Simulation results demonstrate that the proposed algorithm can be used for efficient identification and execution of probabilistically safe paths in real-time.

Adaptive Optimal Path Following for High Wind Flights

Abstract Unmanned aerial vehicle path following is addressed as an infinite horizon regulator problem. Using the linear quadratic regulator technique an optimal guidance law is derived. The state weighting matrix is chosen as a function of the position error and this adaptive nature of the cost function controls the UAV errors tightly. Numerical simulations are carried out for straight line and circular paths under various wind conditions. Results show considerably lower position errors as compared to an existing guidance law. Path following with winds up to half the vehicle airspeed is achieved.

UAV Path Following in Windy Urban Environments

This paper considers UAV path following in cluttered environments under windy conditions. Unstructured wind patterns in cluttered environments can make path following difficult resulting in high errors and possibly collisions with buildings. Combining a pursuit guidance law philosophy with a line-of-sight guidance law, we develop a novel guidance law that has low computational complexity and can track straight line paths, circular paths, a combination of both and waypaths accurately in the presence of wind blowing as high as fifty percent of the UAV’s air speed. Performance of the guidance law is demonstrated through numerical simulations.

A Suboptimal Path Planning Algorithm Using Rapidly-exploring Random Trees

This paper presents path planning algorithms using Rapidly-exploring Random Trees (RRTs) to generate paths for unmanned air vehicles (UAVs) in real time, given a starting location and a goal location in the presence of both static and pop-up obstacles. Generating near optimal paths in obstacle rich environments within a given short time window is a challenging task. Hence we first generate a path quickly using RRT by taking the kinematic constraints of the UAV into account. Then we develop an anytime algorithm that yields paths whose quality improves as computation time increases. When the UAV detects a pop-up obstacle the path planner re-generates a new path from its current location. In order to track a generated path, an effective guidance law with a switching mechanism based on pursuit and line of sight guidance laws is developed. Simulation studies are carried out to demonstrate the performance of the proposed algorithm.

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.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

Flight dynamics and nonlinear control design for variable-pitch quadrotors

This paper introduces the mathematical model for quadrotor with variable-pitch propellers that facilitates generation of negative thrust, thereby augmenting the rate of change of thrust generation suitable for aggressive maneuvering. Blade element theory along with momentum theory is used to estimate aerodynamic loads essential for formulating rigid body dynamics model of the vehicle. Further, the paper develops a nonlinear controller using dynamic inversion technique to stabilize and/or to track a reference trajectory. The controller uses three loops. The outer loop solves the translation dynamics to generate the thrust, pitch angle, and roll angle commands required to achieve a given state or trajectory. Using the commands generated in the outer loop, the inner loop simplifies the rotational dynamics to provide the desired angular velocities. The control allocation loop is added to address the nonlinear relation between control input and rotor thrust and torque. This is done by introducing the derivative of thrust coefficient as a virtual control to the system. These virtual inputs control the derivatives of thrust and body moments, which in turn generates the required thrust and body moments. The performance of the proposed design is shown through simulated results for attitude stabilization and trajectory following.

A cooperative pursuit-evasion game of a high speed evader

This paper studies a pursuit-evasion game of multiple pursuers and a high speed evader for holonomic systems. A group of pursuers uses the idea of perfectly encircled formation to capture an evader. The perfectly encircled formation is a formation in which an evader does not have an instantaneous escape path and it is defined using the concept of Apollonius circle. The paper initially presents the conditions required to create a perfectly encircled formation. It is then argued that if a perfectly encircled formation shrinks over time by maintaining the connectivity between the Apollonius circles, then capture is guaranteed. This paper shows that it is not possible to maintain the connectivity while shrinking with minimum number of pursuers. Hence in this case, the capture can not be guaranteed. An escape strategy is suggested that enables an evader to escape from the perfectly encircled formation. The proposed escape strategy is evaluated through numerical simulations and future directions are discussed.