Andrew T. Klesh

Solar-Powered Aircraft: Energy-Optimal Path Planning and Perpetual Endurance

This paper considers energy-optimal path planning and perpetual endurance for unmanned aerial vehicles equipped with solar cells on the wings, which collect energy used to drive a propeller. Perpetual endurance is the ability to collect more energy than is lost during a day. This paper considers two unmanned aerial vehicle missions: 1) to travel between given positions within an allowed duration while maximizing the final value of energy and 2) to loiter perpetually from a given position, which requires perpetual endurance. For the first mission, the subsequent problem of energy-optimal path planning features the coupling of the aircraft kinematics and energetics models through the bank angle. The problem is then formulated as an optimal control problem, with the bank angle and speed as inputs. Necessary conditions for optimality are formulated and used to study the optimal paths. The power ratio, a nondimensional number, is shown to predict the qualitative features of the optimal paths. This ratio also quantifies a design requirement for the second mission. Specifically, perpetual endurance is possible if and only if the power ratio exceeds a certain threshold. Comparisons are made of this threshold between Earth and Mars. Implications of the power ratio for unmanned aerial vehicle design are also discussed. Several illustrations are given.

Path planning for cooperative time-optimal information collection

Motivated by cooperative exploration missions, this paper considers constant velocity, level flight path planning for Unmanned Air Vehicles (UAVs) equipped with range limited, omni-directional sensors. These active energy-based sensors collect information about objects of interest at rates that depend on the range to the objects according to Shannons channel capacity equation, where the signal-to-noise ratio is governed by the radar equation. The mission of the UAVs is to travel through a given area and collect a specified amount of information about each object of interest while minimizing the total mission time. This information can then be used to classify the objects of interest. An optimal path planning problem is formulated where the states are the Cartesian coordinates of the UAVs and the amounts of information collected about each object of interest, the control inputs are the UAV heading angles, the objective function is the total mission time, and the boundary conditions are subject to inequality constraints that reflect the requirements of information collection. Necessary conditions for optimality are given, whose solutions yield extremal paths, and whose utilization highlights analytical properties of these extremal paths. The problem exhibits several limiting regimes, including the so-called Watchtower and the Multi-Vehicle Traveling Salesman Problem. These results are illustrated on several time-optimal cooperative exploration scenarios.

Energy-Optimal Path Planning for Solar-Powered Aircraft in Level Flight

[Abstract] Motivated by long-endurance requirements in surveillance, reconnaissance and exploration, this paper considers level flight path planning for unmanned aerial vehicles (UAVs) equipped with solar cells on the upper surface of the wings. These solar cells collect energy that is stored in a battery and used to drive a propeller. The mission of the UAV is to travel from a given initial position to a given final position, in less than an allowed duration, using energy from the battery. The subsequent problem of energy-optimal path planning features the interaction between the aircraft kinematics, the energy collection model, and the energy loss model. All three models are coupled by the bank angle of the UAV. Within this framework, the problem is formulated as an optimal path planning problem, with the aircraft bank angle and speed serving as control inputs. Necessary conditions for optimality are given, whose solution yields extremal paths. These necessary conditions are utilized to study analytically the properties of extremal paths. An ecient numerical procedure is also given. It is shown that optimal paths belong to one of two regimes: solar or drag. The Power Ratio, a non-dimensional number that can be computed before flight, is identified. It is shown that this ratio predicts the regime of the optimal path, which facilitates the solution. Implications of the power ratio for UAV design are discussed. Several illustrations are given.

INSPIRE: Interplanetary NanoSpacecraft Pathfinder in Relevant Environment

The INSPIRE project would demonstrate the revolutionary capability of deep space CubeSats by placing two nanospacecraft in Earth-escape orbit. Prior to any inclusion on larger planetary missions, CubeSats must demonstrate that they can operate, communicate, and be navigated far from Earth – these are the primary objectives of INSPIRE. Spacecraft components, such as a JPL X-band radio and a robust watchdog system, would provide the basis for future high-capability, lower-cost-risk missions beyond Earth. These components should enable future supplemental science and educational opportunities at many destinations. The nominal INSPIRE mission would last for three months and achieve an expected Earth-probe distance of 1.5x10 km (dependent upon escape velocity as neither spacecraft will have propulsion capability). The project would monitor onboard telemetry; operate, communicate, and navigate with both spacecraft; demonstrate cross-link communications; and demonstrate science utility with an onboard magnetometer and imager. Lessons learned from this pathfinder mission should help to inform future interplanetary NanoSpacecraft and larger missions that might use NanoSpacecraft components.

Periodic Energy-Optimal Path Planning for Solar-Powered Aircraft

[Abstract] This paper considers energy-optimal path planning in a loitering mission for solar-powered unmanned aerial vehicles (UAVs) which collect solar energy from the sun to power their ight. We consider ascending and descending ight maneuvers in a periodic mission constrained to the surface of a vertical cylinder. The coupling of the aircraft kinematic and energetic models is treated in a novel scheme that implements both the periodic and cylindrical constraints. Optimum trajectories are identied by specifying the heading angle and altitude by periodic splines. Given the periodic splines, we are able to solve for the other aircraft parameters, including the aerodynamic, propulsive, and energetic properties of the aircraft. In an example problem, trajectories are obtained that generate better energy properties than those given by constant altitude circular ight. Numerical simulation results are presented that help demonstrate the properties of the optimum trajectories.

Cyber-Physical Challenges for Space Systems

Modern space systems necessarily have a tight coupling between onboard cyber (processing, communication) and physical (sensing, actuation) elements to survive the harsh extraterrestrial environment and successfully complete ambitious missions. This article first summarizes space exploration missions and existing platforms that to-date have been developed by ad hoc, one-of-a-kind cyber-physical integration efforts. The primary goal of this paper is to present a series of cyber-physical systems (CPS) challenges that, if addressed in the emerging science of CPS, will greatly facilitate complex space systems development in the future. Areas of focus include spacecraft communications, driven by relative orbiting network node positions as well as bandwidth and power considerations, attitude control and orbit determination, and space robotics and science payload systems. A strong CPS challenge problem is introduced: scheduling the instructions executed on a small spacecraft processor such that the magnetic field introduced by this processor induces torques favorable for spacecraft pointing.

Models and Tools to Evaluate Space Communication Network Capacity

This paper introduces models and tools to assess the communication capacity for highly dynamic and geographically diverse ground stations that loosely collaborate to provide increased satellite connectivity. Communication capacity is the total amount of information exchanged between a network of satellites and ground stations over a finite time period. We outline the major constraints on communication capacity which influence transmission capabilities from the satellite, ground station, and network perspectives. Orbit models are combined with engineering analysis software to compare the capacity of existing and future ground station networks. Simulation results from recent clustered satellite launches and representative ground networks are presented and the capacity properties are discussed. By studying network communication capacity, we find opportunities to optimize communication schedules across federated networks to simultaneously and autonomously support multiple satellites.

Optimal path planning for uncertain exploration

Exploration always occurs in the presence of uncertainty. In this paper, we consider path planning for autonomous vehicles equipped with range-based sensors and traveling in an uncertain area. The mission of the vehicles is to explore a set of objects of interest while reducing uncertainty in object position, visibility and state. A connection is shown between the Kalman filter (used to reduce uncertainty) and the so-called Shannon model for exploration through the use of a range-based covariance. This connection is exploited to estimate states and to travel between objects of interest. A bound on the covariance error and several illustrative examples are provided.

Optimal Cooperative Thermalling of Unmanned Aerial Vehicles

Motivated by cooperative exploration missions, this chapter considers the use of thermals to increase the altitudes of multiple unmanned aerial vehicles (UAVs). The mission of the UAVs is to travel through a given area and identify updrafts. The UAVs communicate to each other the location of each rise or fall in their altitude to form a map of the area. This imperfect map can then be used to identify areas of interest that may be potential thermals. The subsequent problem of utilizing these thermals is addressed from the viewpoint of information collection based on Shannon’s channel capacity equation. This method yields paths that achieve the intended result, to elevate the aircraft to higher altitudes, while benefiting from cooperation. Several illustrations are given.

A Reconfigurable Flight Management System for Small-Scale Unmanned Air Systems

Unmanned air systems are becoming increasingly pervasive in academia as well as industry. Aerospace research and education have to-date focused on the fundamental aerodynamics, structures, and control technologies required for these systems, typically relying on commercial avionics packages to provide the hardware and baseline software needed for unmanned vehicle flight testing. This paper describes an ongoing effort at the University of Michigan to design, implement, and adapt to multiple platforms an open-source, reconfigurable flight management system. Emphasis has been placed on modularity and extensibility, resulting in a system that equally addresses Aerospace education and research challenges. This paper overviews the avionics and software design, implementation, and testing processes completed to-date. Use of the University of Michigan Flight Management System (UM-FMS) to support education in software engineering, embedded instrumentation, and multi-layer control is discussed, along with adaptation to specific flight vehicles.