ESA’s SWARM constellation of three near-polar satellites was launched on 22 November 2013, with the primary scientific objective to map the Earth’s magnetic field and its variations. Although not among its primary scientific objectives, the specific orbital formation geometry of the three identical SWARM accelerometer-equipped satellites allows recovery for more accurate low-degree temporal gravity field. Equipped with satellite laser ranging retro-reflectors, accelerometers and geodetic-quality GPS receivers, data from the SWARM satellites have been used to estimate low-degree temporal gravity field based on the acceleration, short-arc, and celestial mechanics approaches, with geopotential solutions complete to degree and order 15. Here we will use the improved formulation for the energy balance approach (EBA) to estimate the temporal gravity field using data from the SWARM satellites. The improved energy balance approach to generate in situ geopotential difference measurements using the GRACE KBR data has achieved the measurement accuracy by more than 3 orders of magnitude compared to previous studies. Specifically, we will: (1) assess the accuracy of SWARM temporal gravity field EBA solutions by comparing with solutions using other approaches and versus GRACE solutions using GPS and using KBR; (2) assess the impact on lowdegree temporal gravity field EBA solutions using kinematic or dynamic SWARM GPS orbits; (3) evaluate low-degree temporal gravity solutions with or without accelerometer-corrections for data from individual SWARM satellite or from the combined constellation of SWARM satellites; (4) evaluate and confirm the maximum achievable degree and order of temporal gravity field model using data from the SWARM constellation of satellites, and (5) investigate the fidelity of the estimated SWARM second degree zonal geopotential coefficients and other approaches, as well as the solutions using other data, including SLR, other GPS, and GRACE KBR solutions.

We present a general solution for steering microrobotic
swarm by dynamic actuating fields. In our approach, the
motion of micro-robots is controlled by changing the actuating
direction of a field applied to them. The time-series sequence
of actuating field’s directions can be computed automatically.
Given a target position in the domain of swarm, a governing
field is first constructed to provide optimal moving directions at
every points. Following these directions, a robot can be driven
to the target efficiently. However, when working with a crowd of
micro-robots, the optimal moving directions on different agents
can contradict with each other. To overcome this difficulty, we
develop a novel steering algorithm to compute a statistically
optimal actuating direction at each time frame. Following a
sequence of these actuating directions, a crowd of micro-robots
can be transported to the target region effectively. Our steering
strategy of swarm has been verified on a platform that generates
magnetic fields with unique actuating directions. Experimental
tests taken on aggregated magnetic micro-particles are quite
encouraging.