This paper presents a new approach to guaranteeing collision avoidance with respect to moving obstacles that have constrained dynamics but move unpredictably. Velocity Obstacles have been used previously to plan trajectories that avoid collisions with obstacles under the assumption that the trajectories of the objects are either known or can be accurately predicted ahead of time. However, for real systems this predicted trajectory will typically only be accurate over short time-horizons. To achieve safety over longer time periods, this paper instead considers the set of all reachable points by an obstacle assuming that the dynamics fit the unicycle model, which has known constant forward speed and a maximum turn rate (sometimes called the Dubins car model). This paper extends the Velocity Obstacle formulation by using reachability sets in place of a single "known" trajectory to find matching constraints in velocity space, called Velocity Obstacle Sets. The Velocity Obstacle Set for each obstacle is equivalent to the union of all velocity obstacles corresponding to any dynamically feasible future trajectory, given the obstacle's current state. This region remains bounded as the time horizon is increased to infinity, and by choosing control inputs that lie outside of these Velocity Obstacle Sets, it is guaranteed that the host agent can always actively avoid collisions with the obstacles, even without knowing their exact future trajectories. Furthermore it is proven that, subject to certain initial conditions, an iterative planner under these constraints guarantees safety for all time. Such an iterative planner is implemented and demonstrated in simulation.

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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...

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