Admissible Subspace TRajectory Optimizer (ASTRO) for Autonomous Robot Operations on the Space Station

Abstract

This paper presents the development of a real-time path-planning optimization approach to controlling the motion of space-based robots. The algorithm is capable of designing a trajectory for a robot to navigate within complex surroundings that include numerous obstacles (generalized shapes) and constraints (geometric and performance limitations). The methodology employs a unique transformation that effectively changes a complex optimization problem into one with a positive definite cost function that enables high convergence rates for complex geometries, enabling its application to real-time operations. This strategy was implemented on the Synchronized Position Hold Engage Reorient Experimental Satellite (SPHERES) test-bed on the International Space Station (ISS), and iterative experimental testing was conducted onboard the ISS during Expedition 17 by the first author.

Trajectory Optimization for Proximity Operations Around Tumbling Geometrical Constraints via Legendre Polynomials

“…The general theory behind the ASTRO guidance algorithm is summarized here for completeness. For a more detailed derivation of the theory, the reader is referred to the work of Chamitoff et al 15 The key feature of the ASTRO algorithm is its ability to optimize a trajectory-related cost function by projecting its gradient onto the subspace of parametric variation that enforces the boundary conditions. Hence, subsequent iterations move closer to a solution that satisfies all constraints.…”

“…14 Another recent solution to the nonlinear constrained optimization problem is a guidance law termed Admissible Subspace Trajectory Optimizer (ASTRO), which consists of an optimal / sub-optimal collision avoidance path-planning strategy that also considers spacecraft performance restrictions. 15 ASTRO transforms the problem into a parameter space that is well behaved; it can navigate complex surroundings with multiple obstacles and constraints. This ASTRO algorithm was implemented and tested on the International Space Station (ISS) Synchronized Position Hold Engage Re-orient Experimental Satellites (SPHERES).…”

“…The original ASTRO algorithm was experimentally validated through the ISS-SPHERES testbed, by executing a compiled version of the algorithm in MATLAB while commanding the SPHERES satellite via wireless command link at one second intervals. 15 The computation of the trajectory could however take up to ten seconds to complete. The original development considered a spherical object traveling with varying velocities within cylindrical corridors in close proximity to elementary spherical or cylindrical obstacles.…”

Locomotion speed capability analysis of six-legged robots: Optimization and application

“…When N is larger than two, highdimensional search methods need to be applied. Chamitoff et al 11 parameterized the trajectory by Legendre polynomials using 3 N unknown parameter and used convex optimization to search the optimal solution. Gasparetto et al 12,13 utilized the time of N waypoints to describe the trajectory by cubic spline and fifth-order B-spline, and solved it with a branchand-bound procedure.…”

Flight Results of Vision-Based Navigation for Autonomous Spacecraft Inspection of Unknown Objects

“…The main benefit of this simplicity is that, if implemented correctly, this algorithm can have very low computational cost. As a result, it can run as a higher-frequency background control process, ensuring safe relative positioning, while more complicated mapping and planning algorithms (e.g., those found in [12][13][14][15][16][17]) are being run ahead of close proximity and docking operations. Alternatively, this relative navigation and control system can be used with a very low power embedded computer (possibly on a very small satellite) to perform an inspection mission at a safe keepout distance.…”