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Formation Control

This task develops the formation control architectures, algorithms and dynamic models needed to plan optimal formation trajectories for next-generation science missions and to ensure that these trajectories are precisely tracked while avoiding collisions, minimizing and balancing fuel consumption, and minimizing sensing and communication requirements.

Task Objective

The objective of this WA is to develop and demonstrate formation architectures, integrated guidance, control, and estimation algorithms, and formation dynamic models for precision, autonomously-supervised, small-to-moderately sized formations in both Earth-orbit and deep space.

Statement of Work

  • Develop 3 and 6 DOF formation guidance algorithms
  • Develop scaleable formation estimation algorithms
  • Develop formation flying control algorithms
  • Develop modeling architectures of formation dynamics

Task Description

Develop and demonstrate formation architectures, integrated guidance, control, and estimation algorithms, and formation dynamic models for precision, autonomously-supervised, small-to-moderately sized formations in both Earth-orbit and deep space

Formation flying spacecraft refers to a set of spatially distributed spacecraft whose dynamic states are coupled through a common control law. This coupling enables the set of spacecraft to interact and function collaboratively. See Figure 1. Several of NASA’s future Earth and Space science missions involve formation flying of multiple coordinated spacecraft.

For Earth science applications, formation flying (FF) spacecraft can provide distributed sensing for gravitational field mapping, contemporaneous spatial sampling of atmospheric data, co-observations (i.e., near-simultaneous observations of the same science target by instruments on multiple platforms), and synthetic radio-frequency and radar apertures. In particular, it will become possible to expand our science capabilities by deploying large numbers of low cost, Earth-orbiting miniaturized spacecraft. An added advantage of this paradigm is that new formation members can be introduced expand or upgrade the formation, or to replace a failed member.

images of spacecraft as described in the caption that follows
Figure 1. Spacecraft Formations in Deep Space and Earth Orbit

Similarly, several space science missions include either distributed instruments, large phased arrays of lightweight reflectors and antennas, or variable baseline space interferometers. For example, synthetic apertures composed of multiple collector and combiner spacecraft will image the event horizon of a black hole, study stellar evolution, and search for Earth-like planets circling other stars and probe their atmospheres for indications of life. Figure 2 shows the proposed black hole-imaging formation MAXIM. Included in Figure 2 is a possible predicted image of the black hole suspected to be at the center of Galaxy M87.

Maxim related images and diagram, as described in the caption that follows
Figure 2. Micro-Arcsecond X-Ray Imaging Mission (MAXIM) Formation Concept and Example Science Return1

A new set of critical requirements is emerging out of the distributed spacecraft mission architecture that goes beyond traditional single spacecraft attitude guidance and control. By its very nature distributed spacecraft missions (especially the deep space science missions) require:

  • Collision free operation, even under fault scenarios
  • Robust lost-in-space initialization, i.e., the ability to establish relative sensor measurements and inter-spacecraft communication after initial formation deployment or after reset/recovery events
  • Optimal path planning in both attitude and translation under multiple constraints (e.g. solar, thermal, glint, hardware capability)
  • Consumable resource balancing across all spacecraft
  • Precision formation control coordinated across multiple spacecraft, i.e., relative positions are controlled to the centimeter level or better, and attitudes are controlled to the arc-minute level or better
  • Observation-on-the-fly capability to enable continuous science measurements during formation maneuvers, i.e., synchronized actuation across a formation to ensure self-generated disturbances do not corrupt science measurements
  • Autonomous operation: the formation can be commanded as a single unit, with lower level, individual spacecraft actions derived from higher-level commands

These new, distributed spacecraft requirements must be met under traditional single spacecraft-level constraints and new, formation-level constraints. For example, optimal formation guidance algorithms must still account for individual spacecraft pointing constraints (e.g. star tracker field-of-view must exclude the Sun), but now must also account for spacecraft-to-spacecraft glint and thermal constraints (i.e., the hot sun-shield of one formation member cannot thermally irradiate the cryogenic payload of another). In these examples, spacecraft attitudes and relative positions are coupled: formation guidance is naturally a six degree-of-freedom problem. This rotational/translational coupling is a common aspect of formation guidance and estimation problems.

The requirements and constraints which apply to a given formation depend upon the operational phase of that formation. A formation’s operations can be divided into three high-level phases: 1) formation initialization, 2) science observation, and 3) formation reconfiguration. Formation initialization is the process of using on-board hardware to autonomously establish inter-spacecraft communications and measure relative spacecraft positions for control. The latter part, measuring relative spacecraft positions, is particularly important for deep space formations, which are beyond the reach of the Global Positioning System. This relative position measurement phase is illustrated in Figure 3.

Spacecraft alignment as described in the caption that follows Figure 3. Initialization (Relative Position Measurement): on-board, limited field-of-view relative sensors must simultaneously “lock” to obtain a measurement. While spacecraft 3 is in the field-of-view of spacecraft 1, the reverse is not true, and so there is no measurement (grey cone). However, spacecraft 1 and 2 see each other simultaneously, and so there is a measurement (green cones).

As the name suggests, the science observation phase consists of formation maneuvers that are necessary to carry out a formation’s primary science objective. For example, a tetrahedron formation can be used to measure the gradients of the Earth’ magnetic field or a formation can be rotated as a virtual rigid body, which requires synchronized relative positions and attitudes. See Figure 4. Another example, shown in Figure 5, is planning a “u,v-Coverage” for a synthetic aperture image.

Figure 4. Formation Rotations: rotating the formation as a virtual rigid body

two diagrams of formation rotations

Diagram of a set of relative spacecraft positions Figure 5. u,v-Coverage: a path through a set of relative spacecraft positions (u,v-points) that leads to the desired synthetic aperture performance

Formation reconfiguration is the least structured and most complex operational phase. It consists of formation maneuvers that are needed to move a formation from its current configuration to the configuration needed for the next science observation. For example, a synthetic aperture formation can be rotated as a virtual rigid body to observe a new star, or an Earth-observing sparse antenna array can reconfigure its constituent spacecraft to form two sub-apertures with different wavelengths and baselines. See Figure 6.

Figure 6. Formation Reconfiguration: changing the synthetic antenna diameter for a low Earth orbit sparse array antenna formation


Watch: DARPA Formation Control V3

Illustration of a formation reconfiguration

This task develops integrated precision formation estimation, guidance and control architectures and algorithms for each of these three operational phases subject to the requirements and constraints discussed previously. Formation dynamic models that are the basis for analytic developments and precision performance validation are also developed. Note that integrated algorithms are needed since, similar to the rotational/translational coupling mentioned previously, estimation, guidance and control functions can be coupled. For example, a formation control algorithm’s ability to tolerate delay affects the latency requirements for communicated measurements in a formation estimator.

Diagram of formation control architecture
Figure 7. Leader/Follower Formation Control Architecture

Due to the distributed nature of a formation, FF architectures are being developed to support flexible, scalable, and robust sensing, communication and control capabilities (e.g. communication latencies, intermittent loss of lock of relative sensors, and asynchronous spacecraft). In terms of robustness, analytical redundancy within the control and estimation architectures is necessary to retain functionality even in the face of hardware failures. Such analytical redundancy can be utilized to, for example, autonomously implement translation maneuvers under a limited set of thruster failures or maintain formation control in the presence of intermittent loss of relative sensing during formation reconfigurations.


The precision formation architectures and algorithm developed in this task will be (and have been) demonstrated in appropriate test environments. A selection of the developed algorithms will be (and have been) demonstrated in a distributed, real-time simulation environment. Select algorithms will also be demonstrated in the 6 degree of freedom, robotic Formation Control Testbed (FCT). The FCT, which is nearing completion, uses flight-like hardware and will allow validation of algorithms to the centimeter/arcminute level required by precision formations.

1 Images courtesy of Keith Gendreau, Webster Cash, Ann Shipley, and Nick White at and NASA/STScI at

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