Daniel P. Scharf

A survey of spacecraft formation flying guidance and control (part 1): guidance

This paper provides a comprehensive survey of spacecraft formation flying guidance (FTG). Here by the term guidance we mean both path planning and optimal, open loop control design.

Minimum-Landing-Error Powered-Descent Guidance for Mars Landing Using Convex Optimization

To increase the science return of future missions to Mars and to enable sample return missions, the accuracy with which a lander can be deliverer to the Martian surface must be improved by orders of magnitude. The prior work developed a convex-optimization-based minimum-fuel powered-descent guidance algorithm. In this paper, this convex-optimization-based approach is extended to handle the case when no feasible trajectory to the target exists. In this case, the objective is to generate the minimum-landing-error trajectory, which is the trajectory that minimizes the distance to the prescribed target while using the available fuel optimally. This problem is inherently a nonconvex optimal control problem due to a nonzero lower bound on the magnitude of the feasible thrust vector. It is first proven that an optimal solution of a convex relaxation of the problem is also optimal for the original nonconvex problem, which is referred to as a lossless convexification of the original nonconvex problem. Then it is shown that the minimum-landing-error trajectory generation problem can be posed as a convex optimization problem and solved to global optimality with known bounds on convergence time. This makes the approach amenable to onboard implementation for real-time applications.

Flight-Like Ground Demonstrations of Precision Maneuvers for Spacecraft Formations—Part II

Formations of collaborating spacecraft enable orders-of-magnitude increases in Earth and space science. However, to realize robust, high-performance formations, the complex interactions of distributed guidance, estimation, control, sensing, actuation, and inter-spacecraft communication must be addressed. As in any technology development, such interactions are first dealt with through analysis and simulation. Then system-level, hardware-based demonstrations are needed to validate simulations and provide the technological maturity necessary to proceed with flight demonstrations and, eventually, a mission. This paper and its companion describe such a maturation process and system-level hardware demonstration results for the formation flying control system of NASAs Terrestrial Planet Finder Interferometer (TPF-I). In this paper, first technology and testbed needs are discussed for system-level validation of precision formation control systems. Then the Formation Control Testbed (FCT) is described in detail. The FCT is a ground-based, robotic environment for high-fidelity, six degree-of-freedom validation with flight-like hardware. Finally, the formation control architecture and synchronized rotation guidance algorithm used in the precision formation flying demonstrations are presented. The companion paper gives all the experimental results, traces the ground performance demonstrated to TPF-I flight performance through a simulation-based error budget, and highlights some technology areas for further development.

Customized Real-Time Interior-Point Methods for Onboard Powered-Descent Guidance

This paper presents a new onboard-implementable, real-time convex optimization-based powered-descent guidance algorithm for planetary pinpoint landing. Earlier work provided the theoretical basis of convexification, the equivalent representation of the fuel-optimal pinpoint landing trajectory optimization problem with nonconvex control constraints as a convex optimization problem. Once the trajectory optimization problem is convexified, interior-point method algorithms can be used to solve the problem to global optimality. Though having this guarantee of convergence motivated earlier convexification results, there were no real-time interior point method algorithms available for the computation of optimal trajectories on flight computers. This paper presents the first such algorithm developed for onboard use and flight-tested on a terrestrial rocket with the NASA Jet Propulsion Laboratory and the NASA Flight Opportunities Program in 2013. First, earlier convexification results are summarized and the result...

Terrestrial Planet Finder Interferometer: 2007-2008 Progress and Plans

This paper provides an overview of technology development for the Terrestrial Planet Finder Interferometer (TPF-I). TPF-I is a mid-infrared space interferometer being designed with the capability of detecting Earth-like planets in the habitable zones around nearby stars. The overall technology roadmap is presented and progress with each of the testbeds is summarized.

Dynamics of Earth Orbiting Formations

In this paper the equations of motion of a formation consisting of n spacecraft in Earth orbit are derived via Lagrange’s equations. The equations of motion of the formation are developed with respect to both (1) a bound Keplerian reference orbit, and (2) a specific spacecraft in the formation. The major orbital perturbations acting on a formation in low Earth orbit are also included in the analysis. In contrast to the traditional approach based on the balance of linear momentum, the use of Lagrange’s equations leads to a high-level matrix derivation of the formation equations of motion. The matrix form of the nonlinear motion equations is then linearized about a bound Keplerian reference orbit. Next, it is demonstrated that under the assumption of a circular reference orbit, the linearized equations of motion reduce to the well-known Hill-Clohessy-Wiltshire equations. The resulting linear and nonlinear dynamic equations lead to maximal physical insight into the structure of formation dynamics, and are ideally suited for use in the design and validation of formation guidance and control laws.

Guaranteed initialization of distributed spacecraft formations

In this paper we present a solution to the formation initialization (FI) problem for N distributed spacecraft located in deep space. Our solution to the FI problem is based on a three-stage sky search procedure that reduces the FI problem for N spacecraft to the simpler problem of initializing a set of sub-formations. An analytical proof demonstrating that our algorithm guarantees formation initialization for N spacecraft constrained to a single plane is presented. An upper bound on the time to initialize a planar formation is also provided. We then demonstrate our FI algorithm in simulation using NASA’s v e-spacecraft Terrestrial Planet Finder mission as an example.

ADAPT demonstrations of onboard large-divert Guidance with a VTVL rocket

The Autonomous Ascent and Descent Powered-Flight Testbed (ADAPT) is a closed-loop, free-flying testbed for demonstrating descent and landing technologies of next-generation planetary landers. The free-flying vehicle is the Masten Space Systems Xombie vertical-takeoff, vertical-landing suborbital rocket. A specific technology ADAPT is demonstrating in the near-term is Guidance for Fuel-Optimal Large Diverts (G-FOLD), a fuel-optimal trajectory planner for diverts during powered descent, which is the final kilometers of descent to landing on rocket engines. Previously, ADAPT used Xombie to fly optimal large-divert trajectories, extending Xombies divert range to 750 m. However, these trajectories were planned off-line with G-FOLD. This paper reports the successful Xombie flight demonstrations of large diverts using G-FOLD on board to calculate divert trajectories in real time while descending. The culminant test flight of the last year was an 800 m divert that was initiated at an altitude of 290 m while moving away from and crosswise to the landing pad. Hence, G-FOLD had to calculate a constrained divert trajectory that reversed direction, was fully three-dimensional, with horizontal motion nearly three times the initial altitude, and it did so in ~100 ms on board Xombie as it was descending. Xombie then flew the divert trajectory with meter-level precision, demonstrating that G-FOLD had planned a trajectory respecting all the constraints of the rocket-powered vehicle. The steps to reach this flight demonstration of on-board generation of optimal divert trajectories and the system engineering for future ADAPT payloads are also presented.

Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

An overview of formation flying technology development for the Terrestrial Planet Finder mission

The objective of the Terrestrial Planet Finder (TPF) mission is to find and characterize earth-like planets orbiting other stars. Three architectural options are under consideration for this mission: a formation-flying interferometer (FFI), a structurally-connected interferometer, and a coronagraph. One of these options can be selected as the TPF baseline design in 2006. This paper describes the technology tasks underway to establish the viability of precision formation flying for the FFI option. In particular, interferometric science observations require autonomous precise control and maneuvering of five spacecraft to an accuracy of 2 cm in range and 1 arc-minute in bearing. This precision must be maintained over interspacecraft ranges varying from a few meters to hundreds of meters. Autonomous operations, ranging from formation acquisition and formation maneuvering to high precision formation flying during science observations, are required. Challenges lie in meeting the demanding performance requirements as well as in demonstrating the long-term robustness of the autonomous formation flying system. These challenges are unprecedented for deep space missions. To address them, research is under way in the areas of formation control algorithms, relative sensor technologies, system design, end-to-end real-time system simulation, and ground-based and micro-g end-to-end system demonstrations. Four interrelated testbeds are under development concurrently with the FFI system design. The testbeds include the formation algorithms & simulation testbed (FAST), the formation sensor testbed (FST), the formation control testbed (FCT) and the synchronized position hold engage re-orient experimental satellites (SPHERES) experiment. Formation flying technologies developed under the StarLight project and the NASA Distributed Spacecraft Technology (DST) program are being leveraged and expanded to meet the TPF requirements. This paper provides an overview of the ongoing precision formation flying technology development activities.