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ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system; and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals.For this mission, accurate pulse timing with an ultra-stable clock, and a drag-free spacecraft with reliable inertial sensor are required. T2L2 has demonstrated the required accurate pulse timing; rubidium clock on board Galileo has mostly demonstrated the required clock stability; the accelerometer on board GOCE has paved the way for achieving the reliable inertial sensor; the demonstration of LISA Pathfinder will provide an excellent platform for the implementation of the ASTROD I drag-free spacecraft. These European activities comprise the pillars for building up the mission and make the technologies needed ready. A second mission, ASTROD or ASTROD-GW (depending on the results of ASTROD I), is envisaged as a three-spacecraft mission which, in the case of ASTROD, would test General Relativity to one part per billion, enable detection of solar g-modes, measure the solar Lense-Thirring effect to 10 parts per million, and probe gravitational waves at frequencies below the LISA bandwidth, or in the case of ASTROD-GW, would be dedicated to probe gravitational waves at frequencies below the LISA bandwidth to 100 nHz and to detect solar g-mode oscillations. In the third phase (Super-ASTROD), larger orbits could be implemented to map the outer solar system and to probe primordial gravitational-waves at frequencies below the ASTROD bandwidth. This paper on ASTROD I is based on our 2010 proposal submitted for the ESA call for class-M mission proposals, and is a sequel and an update to our previous paper (Appouchaux et al., Exp Astron 23:491–527, 2009; designated as Paper I) which was based on our last proposal submitted for the 2007 ESA call. In this paper, we present our orbit selection with one Venus swing-by together with orbit simulation. In Paper I, our orbit choice is with two Venus swing-bys. The present choice takes shorter time (about 250 days) to reach the opposite side of the Sun. We also present a preliminary design of the optical bench, and elaborate on the solar physics goals with the radiation monitor payload. We discuss telescope size, trade-offs of drag-free sensitivi...

Nomenclature a = positive parameter a tx a ty a tz T = linear acceleration due to the tether tension, m · s −2 a x a y a z T = linear acceleration of the gripper's thruster force, m · s −2 Ck = matrix in coordinated desaturation controller d = position vector of the capture position, m F l = tether tension, N I = inertia matrix of the combination, kg · m 2 I 0 = nominal value of combination's inertia matrix, kg · m 2 K ξ = positive-definite design matrix k 2 = positive-definite design matrix m = mass of tethered space robot-target combination, kg Ox l y l z l = space tether frame Ox p y p z p = space platform orbital frame Ox t y t z t = combination orbital frame Ox 0 t y 0 t z 0 t = combination body frame P = positive-definite design matrix R = transformation matrix from platform orbital frame to combination body frame Sk = constant positive weighting matrix T l = tether control torque, Nm x y z T = centroid position of the combination in the platform orbital frame, m ΔI = inertia matrix uncertainty, kg · m 2 ε = positive parameter λk = Lagrange multiplier λ L = upper bound of disturbancê λ L = estimation values of disturbance μ = positive design parameter ξ = state of the auxiliary design system σ = modified Rodrigues parameters σ d = desired modified Rodrigues parameters τk = vector of optimal thruster force and tether tension τ c = control torque of the combination, N · m τ d = disturbing torques, N · m τ t = control torque of the thruster, N · m τ l = control torque of the tether, N · m ω = absolute angular velocity of the combination, rad · s −1 ω d = desired angular velocity of the combination, rad · s −1

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In this paper we present a procedure to automatically design and verify the local behavior of robots with highly limited cognition. All robots are: anonymous, homogeneous, noncommunicating, memoryless, reactive, do not know their global position, do not have global state information, and operate by a local clock. They only know: (1) the relative location of their neighbors within a short range and (2) a common direction (North). We have developed a procedure to generate a local behavior that allows the robots to self-organize into a desired global pattern despite their individual limitations. This is done while also avoiding collisions and keeping the coherence of the swarm at all times. The generated local behavior is a probabilistic local state-action map. The robots follow this stochastic policy to select an action based on their current perception of their neighborhood (i.e., their local state). It is this stochasticity, in fact, that allows the global pattern to eventually emerge. For a generated local behavior, we present a formal proof procedure to verify whether the desired pattern will always eventually emerge from the local actions of the agents. The novelty of the proof procedure is that it is primarily local in nature and focuses on the local states of the robots and the global implications of their local actions. A local approach is of interest to reduce the computational effort as much as possible when verifying the emergence of larger patterns. Finally, we show how the behavior could be implemented on real robots and investigate this with extensive simulations on a realistic robot model. To the best of our knowledge, no other solutions exist for robots with such limited cognition to achieve this level of coordination with proof that the desired global property will emerge.