Isaac Kaminer

• PhD
• Professor (Full) at Naval Postgraduate School

Efficient trajectory generation is critical for autonomous systems, yet current numerical methods often struggle to handle periodic behaviors effectively, especially when equidistant time nodes are required. This paper introduces a novel mixed Bernstein-Fourier approximation framework tailored explicitly for optimal motion planning. Our proposed me...

This article presents a novel time-coordination algorithm based on event-triggered communication to ensure multiple UAVs progress along their desired paths in coordination with one another. In the proposed algorithm, a UAV transmits its progression information to its neighbor UAVs only when a decentralized trigger condition is satisfied. Consequent...

A coordinated localization problem is considered between an unmanned aerial vehicle (UAV) and a cooperative unmanned surface vessel (USV) when data from the global positioning system (GPS) is unavailable. The UAV’s task is to gather information about the unknown locations of both cooperative and adversarial USVs. The cooperative USV then uses this...

This paper presents a new connectivity condition on the information flow between UAVs to achieve coordinated path following. The information flow is directional, so that the underlying communication network topology is represented by a time-varying digraph. We assume that this digraph is connected in an integral sense. This is a much more general a...

In this article, a novel time-coordination algorithm based on event-triggered communications is proposed to achieve coordinated path-following of UAVs. To be specific, in the approach adopted a UAV transmits its progression information over a time-varying network to its neighbors only when a decentralized trigger condition is satisfied, thereby sig...

We address the problem of coordinated vision-based tracking of a moving target using multiple unmanned vehicles that exchange information over a supporting time-varying network. The objective of this work is to formulate decentralized control algorithms that enable multiple vehicles to follow the target while coordinating their phase separation. A...

Bernstein polynomial approximation of continuous function has a slower rate of convergence compared to other approximation methods. “The fact seems to have precluded any numerical application of Bernstein polynomials from having been made. Perhaps they will find application when the properties of the approximant in the large are of more importance...

This paper addresses the problem of optimal defense of a high-value unit (HVU) against a large-scale swarm attack. We discuss multiple models for intra-swarm cooperation strategies and provide a framework for combining these cooperative models with HVU tracking and adversarial interaction forces. We show that the problem of defending against a swar...

This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear programming problems. These, in turn, can be solved using off-the-shelf optimization solvers. The mai...

This paper addresses the problem of optimal defense of a High Value Unit against a large-scale swarm attack. We show that the problem can be cast in the framework of uncertain parameter optimal control and derive a consistency result for the dual problem of this framework. We show that the dual can be computed numerically and apply these numerical...

We theoretically and numerically study the problem of optimal control of large-scale autonomous systems under explicitly adversarial conditions, including probabilistic destruction of agents during the simulation. Large-scale autonomous systems often include an adversarial component, where different agents or groups of agents explicitly compete wit...

This article presents a computational framework for planning mine countermeasures (MCM) search missions by autonomous vehicles. It employs generalized optimal control (GenOC), a model-based trajectory optimization approach, to maximize the expected search performance of vehicle–sensor pairs in different minehunting scenarios. We describe each eleme...

This paper presents a computational framework to efficiently generate feasible and safe trajectories for multiple autonomous vehicle operations. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate its solutions in a discretized setting using Bernstein polynomials. The latter possess conveni...

This paper describes and proves the consistency of a flexible numerical method for producing solutions to state and control constrained control problems with parameter dependencies. This method allows for the use of a variety of underlying discretization schemes, which can be catered to differing numerical challenges of specific problems, such as r...

This paper employs a computational optimal control framework which provides trajectory planning for search applications based on specific vehicle and sensor features. With its capability to handle high-dimensional, nonlinear optimal control problems with uncertainty, this framework enables detailed modeling and leveraging of vehicle/sensor features...

The paper addresses the problem of calculating energy optimal trajectory for a novel class of hybrid UAV equipped with hydrogen fuel cell and solar photovoltaic energy production technologies. The objective of the design is to minimize the energy used for propulsion by optimally utilizing the finite energy stored in the onboard hydrogen fuel cell a...

This paper introduces a new concept of partial observability for nonlinear systems. This new approach enables a quantitative analysis on the observability of an individual state variable and unknown parameters of a nonlinear dynamics even when the system is not observable in the traditional sense. The paper develops theoretical properties of partia...

Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been made. Perhaps they will find application when the properties of the approximant in the large are of more import...

This paper investigates optimal glider trajectories for gaining altitude from thermal updraft columns (“thermaling”). Thermal updraft columns provide a natural energy resource that can be beneficial for enabling long-term autonomous soaring objectives. In this paper, computational optimal control is used to investigate possible alternatives to the...

Featured Application Submersed obstacle avoidance in unknown ocean currents via guidance, navigation, and control for autonomous underwater vehicles. Abstract A considerable volume of research has recently blossomed in the literature on autonomous underwater vehicles accepting recent developments in mathematical modeling and system identification;...

This article provides a modeling framework for quantifying cost and optimizing motion plans in combat situations with rapid weapon fire, multiple agents, and attacker uncertainty characterized by uncertain parameters. Recent developments in numerical optimal control enable the efficient computation of numerical solutions for optimization problems w...

This paper focuses on the problem of collision avoidance for Unmanned Aerial Vehicles (UAVs). The dynamics of the UAV are modeled as a Dubins vehicle flying at constant altitude. The angular velocity is used as control input in order to avert a possible collision with a single obstacle, while the speed is left as an extra degree of freedom to achie...

This paper presents a computational framework to efficiently generate feasible and optimal trajectories for differentially flat autonomous vehicle systems. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate it by a discrete-time formulation using Bernstein polynomials. These polynomials al...

Time-Critical Cooperative Control of Autonomous Air Vehicles presents, in an easy-to-read style, the latest research conducted in the industry, while also introducing a set of novel ideas that illuminate a new approach to problem-solving. The book is virtually self-contained, giving the reader a complete, integrated presentation of the different co...

This paper describes a numerical scheme for computing optimal solutions to a class of nonlinear optimal control problems in which parameter uncertainty may be a feature of the state dynamics or objective function. Consistency results are provided for states and controls generated by the algorithm as well as for the adjoint variables.

We are interested in the multiple robot surveillance problem where robots must allocate waypoints to be visited among themselves and plan paths through different waypoints while avoiding obstacles. Furthermore, the robots are allocated specific times to reach their respective goal locations and as a result they have to decide which robot has to vis...

The paper describes the control system development of a novel hybrid autonomous vehicle-Aqua-Quad, a Multi-Rotor Vertical Take Off and Landing aircraft with environmentally hardened electronics, exchangeable sensor suite, communication links, and a solar recharge system. The key objective of this multi-modal autonomous system is to enable energy-aw...

This paper employs a computational optimal control framework to develop a mission planning tool for a team of heterogeneous unmanned vehicles conducting a nominal mine countermeasures (MCM) mission. We first describe our motivation for developing vehicle-specific sensor models for unmanned surface and underwater vehicles working collaboratively to...

The paper describes the control system development of a novel hybrid autonomous vehicle - Aqua-Quad, a Multi-Rotor Vertical Take Off and Landing aircraft with environmentally hardened electronics, exchangeable sensor suite, communication links, and a solar recharge system. The key objective of this multi-modal autonomous system is to enable energy-...

This paper discusses the application of ‘optimal search,’ an optimization framework developed by the US Navy to optimize sonar-based search and rescue operations, to marine mapping tasks. In contrast to path planning methods which focus on maximizing area coverage, optimal search seeks to directly optimize expected sensor performance over a region,...

Multirotor unmanned aerial vehicles (UAVs) have experienced a very fast-paced technological development over the past years. Flight control systems have evolved from simple stability augmentation systems, barely enabling an external pilot to remotely fly a multirotor UAV, to full-fledged command augmentation systems, opening up the possibilities of...

This paper addresses the problem of time-coordination of a team of cooperating multirotor unmanned aerial vehicles that exchange information over a supporting time-varying network. A distributed control law is developed to ensure that the vehicles meet the desired temporal assignments of the mission, while flying along predefined collision-free pat...

We formulate a search-trajectory optimization problem, with multiple searchers looking for multiple targets in continuous time and space, as a parameter-distributed optimal control model. The problem minimizes the probability that all of the searchers fail to detect any of the targets during a planning horizon. We construct discretization schemes a...

We implement and solve a search-trajectory optimization problem originally formulated in our companion paper, with multiple searchers looking for multiple targets in continuous time and space. The problem minimizes the probability that all of the searchers fail to detect any of the targets during a planning horizon. We develop an implementable algo...

This paper describes a multi-vehicle motion control framework for time-critical cooperative missions and evaluates its performance by considering two case studies: a simultaneous arrival mission scenario and a sequential auto-landing of a fleet of UAVs. In the adopted setup, the UAVs are assigned nominal spatial paths and speed profiles along those...

This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evadi...

Coordinated time optimal path planning and trajectory management algorithms for air vehicles depend on precise simultaneous mission commencement by all agents. Ground-based and rotary-wing aerial vehicles can be staged at their mission initial conditions until a mission is commenced but fixed-wing aerial vehicles, which must maintain a minimum forw...

This paper analyzes the stability and convergence properties of a proportional–integral protocol for coordination of a network of agents with dynamic information flow and quantized information exchange. In the setup adopted, each agent is only required to exchange its coordination state with its neighboring agents, and the desired reference rate is...

This paper presents an integrated approach for trajectory generation and time coordination for multiple vehicles, combined with collision avoidance. Pythagorean Hodograph B'ezier curves are used to generate desired feasible trajectories that satisfy the dynamic constraints of the vehicles, and guarantee spatial separation between the paths for safe...

This paper explores the potential for applying newly available numerical methods in optimal control to solve motion planning problems created by the search for targets with motion uncertainty characterized by constant but unknown parameters. These recent developments enable the efficient computation of numerical solutions for search problems with m...

We are interested in the multiple robot surveillance problem where robots must allocate waypoints to be visited among themselves and plan paths through different waypoints while avoiding obstacles. Furthermore, the robots are allocated specific times to reach their respective goal locations and as a result they have to decide which robots have to v...

This paper introduces a heuristic planar trajectory-generation framework for multiple vehicles. Desired feasible trajectories are generated using Pythagorean Hodograph B ́ezier curves that satisfy the dynamic constraints of the vehicles, and guarantee spatial separation between the paths for safe operation. It is shown that the trajectory generatio...

This paper considers the problem of Cooperative Vision Based Tracking of a ground target by a fleet of multiple UAVs. The objective of this work is to present a decentralized control algorithm that enables multiple cooperative vehicles to maintain a horizontal orbital path around the target, while coordinating their space separation. A typical scen...

Time optimal path planning and trajectory management algorithms for air vehicles with limited on-board computing resources require an efficient approach to satisfy flight dynamic constraints needed to guarantee paths are feasible. B-spline curves enable compact definition of feasible airplane trajectories that are suited for on-board real-time comp...

The paper describes the latest advancements in the development of the Rapid Flight Control Prototyping system that were motivated primarily by the need to enable cooperative missions of multiple unmanned aerial vehicles and to enhance the capabilities of human operators to design and oversee the collaborative behaviors of multiple heterogeneous UAV...

This article presents an overview of the application of the Parameter Space Investigation method for the multicriteria design optimization of the L 1 adaptive flight control system implemented on the two turbine-powered dynamically-scaled generic transport model Airborne Subscale Transport Aircraft Research aircraft. In particular, this study addre...

This paper addresses the problem of steering a fleet of unmanned aerial vehicles along desired three-dimensional paths while meeting stringent spatial and temporal constraints. A representative example is the challenging mission scenario where the unmanned aerial vehicles are tasked to cooperatively execute collision-free maneuvers and arrive at th...

This paper analyzes the convergence properties of a distributed proportional-integral protocol for coordination of a network of agents with multiple leaders, dynamic information flow, and quantized measurements. We show that the integral term of the protocol allows the follower agents to 'learn' the reference rate, rather than have it available a p...

This paper focuses on the problem of developing control laws to solve the Time-Coordinated 3D Path-Following task for multiple quadrotor UAVs in the presence of time-varying communication networks and spatial and temporal constraints. The objective is to enable a fleet of quadrotors to track predefined spatial paths while coordinating to achieve sy...

This paper discusses the development and flight testing of an algorithm for cooperative soaring by multiple autonomous gliders. Flight test results confirmed that the algorithm functioned as expected and that the gliders worked cooperatively to find and utilize the same updrafts during the test. However, the flight also indicated that the effective...

This paper focuses on the problem of optimizing the trajectories of multiple searchers attempting to detect a non-evading moving target whose motion is conditionally deterministic. This problem is a parameter-distributed optimal control problem, as it involves an integration over a space of stochastic parameters as well as an integration over the t...

Worldwide, there has been growing interest in the use of autonomous vehicles to execute missions of increasing complexity without constant supervision of human operators. A key enabling element for the execution of such missions is the availability of advanced systems for motion control of autonomous vehicles. Usually, the problems of motion contro...

The University of the Bundeswehr Munich (UBM) and the Naval Postgraduate School (NPS) conduct cooperative research in the field of single operator UAV guidance and ISR payload control. For the first time cognitive automation and Optimal Control elements are combined to join high-level mission guidance with path planning and real-time path following...

This paper addresses the challenge of using autonomous soaring gliders to search for and exploit thermal lift to extend the gliders' endurance. For this purpose, a simple thermal centering controller is proposed. The paper includes theoretical analysis of stability and convergence properties of this controller. Using an exponential Gaussian functio...

This article focuses on the problem of computing a control law for a particular class of tail-sitter aircraft able to switch their flight configuration from hover to level flight and vice-versa. We address the problem of steering a ducted-fan UAV along a given path (path following problem) so as to meet spatial constraints. One possible scenario is...

This paper presents flight-test results that examine the performance and robustness properties of an L 1 control augmentation loop implemented onboard a small unmanned aerial vehicle. The framework used for in-flight control evaluation is based on the Rohrs counterexample, a benchmark problem presented in the early 1980s, to show the limitations of...

This paper addresses the problem of steering an Unmanned Aerial Vehicle along a given path. In the setup adopted, the vehicle is assigned a nominal path and a speed profile along it. The vehicle is then tasked to follow this nominal path independently of the temporal assignments of the mission, which is in contrast to “open-loop” trajectory trackin...

This work extends the earlier results on passive vision-based tracking and motion estimation of a ground vehicle. The follower small unmanned air vehicle (UAV) is equipped with a single gimbaled pan/tilt camera and a high bandwidth wireless link for video and command transmitting. The objective is for the UAV to maintain a horizontal circular orbit...

This paper represents the development of feature following control and distributed navigation algorithms for visual surveillance using a small unmanned aerial vehicle equipped with a low-cost imaging sensor unit. An efficient map-based feature generation and following control algorithm is developed to make an onboard imaging sensor to track a targe...

This paper presents preliminary results of the application of the Parameter Space In-vestigation method for the design of the L1 flight control system implemented on the two turbine-powered dynamically-scaled GTM AirSTAR aircraft. In particular, the study addresses the construction of the feasible solution set and the improvement of a nomi-nal prot...

In this paper the stability and effectiveness of a thermal centering controller for autonomous soaring applications was investigated. The controller was evaluated in flight trials to verify theoretical stability properties obtained in earlier work by the author. The outcome of the trials confirmed stability of the controller under a variety of cond...

This work extends the earlier results of authors on vision-based tracking of a ground vehicle moving with unknown time-varying velocity. The follower UAV is equipped with a single camera. The control objective is to regulate the 2D horizontal range between the UAV and the target to a constant. The extension in this paper has two distinct features....

Certification of adaptive control technologies for both manned and unmanned aircraft represent a major challenge for current Verification and Validation techniques. A (missing) key step towards flight certification of adaptive flight control systems is the definition and development of analysis tools and methods to support Verification and Validati...

The paper presents a three-dimensional path-following control algorithm that expands the capabilities of conventional autopilots, which are normally designed to provide only guidance loops for waypoint navigation. Implementation of this algorithm broadens the range of possible applications of small unmanned aerial vehicles. The solution proposed ta...

There is currently a surge of interest in the development of advanced systems for cooperative control of multiple autonomous marine vehicles. Central to the implementation of these systems is the availability of efficient algorithms for multiple vehicle path planning that can take explicitly into account the capabilities of each vehicle and existin...

The paper summarizes the results of an ongoing effort in the development and flight validation and verification of the metrics driven L1 adaptive flight control system. In particular, the paper develops a unified framework for design, implementation, validation and verification of flight critical control systems including: (i) definition of experim...

This work extends the earlier results of authors on passive vision-based tracking and motion estimation of a non-cooperating ground vehicle. The follower small unmanned air vehicle (UAV) is equipped with a single gimbaled pan/tilt camera and a high bandwidth wireless link for video and command transmitting. The objective is to control the UAV turn...

1 the concept of using cooperating unmanned aerial vehicles (UAVs) to search for thermal lift in order to extend endurance was investigated. This paper elaborates upon this work by including a theoretical analysis of the stability and convergence of the heuristic controller used for centering on thermals. Using an exponential Gaussian function to r...

The paper summarizes the results of an ongoing effort in the development and flight validation and verification of the metrics driven ℒ1 adaptive flight control system. In particular, the paper develops a unified framework for design, implementation, validation and verification of flight critical control systems including: (i) definition of experim...

This paper describes a general framework for the study of multiple vehicle, time-coordinated path following (TC-PF) control problems. An example is the situation where a group of vehicles is tasked to maneuver and arrive at pre-assigned final positions at the same time in a collision-free manner, while reducing some optimality criterion. The time o...

Motivated by increasingly complex and challenging missions at sea, there is widespread interest in the development of advanced systems for cooperative control of multiple autonomous marine vehicles. Central to the implementation of these systems is the availability of efficient algorithms for multiple vehicle path planning that can take explicitly...

One method of improving flight endurance for UAVs is to take advantage of thermal lift occurring in convective boundary layers of the atmosphere. This paper investigates the possible benefits of using a cooperating team of small UAVs to increase the probability of finding thermal lift. An algorithm that employs a team of two autonomous gliders was...

This paper addresses initial steps in the development and flight implementation of a new metrics driven L1 adaptive flight control system. The work primarily focuses on (i) definition of appropriate control driven metrics that account for the control surface failures; (ii) tailoring a recently developed L1 adaptive controller to the design of adapt...

This paper represents an effective optimization approach for building high bandwidth wireless communication networks between distributed autonomous systems using unmanned aerial vehicles as airborne relay nodes. A self-tuning extremum control technique is developed to find an optimal location of the aerial vehicles to provide maximum communication...