Mangal Kothari

Bio: Mangal Kothari is an academic researcher from Indian Institute of Technology Kanpur. The author has contributed to research in topics: Control theory & Computer science. The author has an hindex of 17, co-authored 93 publications receiving 1132 citations. Previous affiliations of Mangal Kothari include University of Porto & National Aerospace Laboratories.

Chance Constrained RRT for Probabilistic Robustness to Environmental Uncertainty

Abstract: 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.

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

Abstract: 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.

Model Predictive Static Programming: A Computationally Efficient Technique For Suboptimal Control Design

Abstract: Combining the philosophies of nonlinear model predictive control and approximate dynamic programming, a new suboptimal control design technique is presented in this paper, named as model predictive static programming (MPSP), which is applicable for finite-horizon nonlinear problems with terminal constraints. This technique is computationally efficient, and hence, can possibly be implemented online. The effectiveness of the proposed method is demonstrated by designing an ascent phase guidance scheme for a ballistic missile propelled by solid motors. A comparison study with a conventional gradient method shows that the MPSP solution is quite close to the optimal solution.

Cooperative target-capturing with inaccurate target information

Abstract: This paper presents distributed formation control of a multi-agent system to encircle a maneuvering target using Lyapunov and graph theories with emphasis on consensus and cooperation. The proposed approach embeds a consensus algorithm into a robust controller to capture a target whose information is partially known. To address this issue, a cooperative strategy in conjunction with a controller is proposed to enable a fleet of UAVs either to escort a target to a desired destination or to keep the target movement restricted in a certain set in order to gain superiority. We have employed a sliding mode controller to achieve a target centered formation whose information is partially available to the capturing vehicles. Simulation results are presented to validate the proposed approach.

Transportation using network of unmanned aerial vehicles

Abstract: Embodiments described herein include a delivery system having unmanned aerial delivery vehicles and a logistics network for control and monitoring In certain embodiments, a ground station provides a location for interfacing between the delivery vehicles, packages carried by the vehicles and users In certain embodiments, the delivery vehicles autonomously navigate from one ground station to another In certain embodiments, the ground stations provide navigational aids that help the delivery vehicles locate the position of the ground station with increased accuracy

Numerical methods for engineers

Abstract: The fifth edition of "Numerical Methods for Engineers" continues its tradition of excellence. Instructors love this text because it is a comprehensive text that is easy to teach from. Students love it because it is written for them--with great pedagogy and clear explanations and examples throughout. The text features a broad array of applications, including all engineering disciplines. The revision retains the successful pedagogy of the prior editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. Approximately 80% of the end-of-chapter problems are revised or new to this edition. The expanded breadth of engineering disciplines covered is especially evident in the problems, which now cover such areas as biotechnology and biomedical engineering. Users will find use of software packages, specifically MATLAB and Excel with VBA. This includes material on developing MATLAB m-files and VBA macros.

Planning for Autonomous Cars that Leverage Effects on Human Actions

Abstract: Traditionally, autonomous cars make predictions about other drivers’ future trajectories, and plan to stay out of their way. This tends to result in defensive and opaque behaviors. Our key insight is that an autonomous car’s actions will actually affect what other cars will do in response, whether the car is aware of it or not. Our thesis is that we can leverage these responses to plan more efficient and communicative behaviors. We model the interaction between an autonomous car and a human driver as a dynamical system, in which the robot’s actions have immediate consequences on the state of the car, but also on human actions. We model these consequences by approximating the human as an optimal planner, with a reward function that we acquire through Inverse Reinforcement Learning. When the robot plans with this reward function in this dynamical system, it comes up with actions that purposefully change human state: it merges in front of a human to get them to slow down or to reach its own goal faster; it blocks two lanes to get them to switch to a third lane; or it backs up slightly at an intersection to get them to proceed first. Such behaviors arise from the optimization, without relying on hand-coded signaling strategies and without ever explicitly modeling communication. Our user study results suggest that the robot is indeed capable of eliciting desired changes in human state by planning using this dynamical system.

Unmanned Aerial Vehicle Path Following: A Survey and Analysis of Algorithms for Fixed-Wing Unmanned Aerial Vehicless

Abstract: Unmanned aerial vehicles (UAVs) are mainly used by military and government organizations, but with low-cost sensors, electronics, and airframes there is significant interest in using low-cost UAVs among aircraft hobbyists, academic researchers, and industries. Applications such as mapping, search and rescue, patrol, and surveillance require the UAV to autonomously follow a predefined path at a prescribed height. The most commonly used paths are straight lines and circular orbits. Path-following algorithms ensure that the UAV will follow a predefined path in three or two dimensions at constant height. A basic requirement for these path-following algorithms is that they must be accurate and robust to wind disturbances.

Probabilistically safe motion planning to avoid dynamic obstacles with uncertain motion patterns

Abstract: This paper presents a real-time path planning algorithm that guarantees probabilistic feasibility for autonomous robots with uncertain dynamics operating amidst one or more dynamic obstacles with uncertain motion patterns. Planning safe trajectories under such conditions requires both accurate prediction and proper integration of future obstacle behavior within the planner. Given that available observation data is limited, the motion model must provide generalizable predictions that satisfy dynamic and environmental constraints, a limitation of existing approaches. This work presents a novel solution, named RR-GP, which builds a learned motion pattern model by combining the flexibility of Gaussian processes (GP) with the efficiency of RRT-Reach, a sampling-based reachability computation. Obstacle trajectory GP predictions are conditioned on dynamically feasible paths identified from the reachability analysis, yielding more accurate predictions of future behavior. RR-GP predictions are integrated with a robust path planner, using chance-constrained RRT, to identify probabilistically feasible paths. Theoretical guarantees of probabilistic feasibility are shown for linear systems under Gaussian uncertainty; approximations for nonlinear dynamics and/or non-Gaussian uncertainty are also presented. Simulations demonstrate that, with this planner, an autonomous vehicle can safely navigate a complex environment in real-time while significantly reducing the risk of collisions with dynamic obstacles.