Two-orbit switch-pitch structures

The Hoberman 'switch-pitch ' ball is a transformable structure with a single folding and unfolding path. The underlying cubic structure has a novel mechanism that retains tetrahedral symmetry during folding. Here, we propose a generalized class of structures of a similar type that retain their full symmetry during folding. The key idea is that we require two orbits of nodes for the structure: within each orbit, any node can be copied to any other node by a symmetry operation. Each member is connected to two nodes, which may be in different orbits, by revolute joints. We will describe the symmetry analysis that reveals the symmetry of the internal mechanism modes for a switch-pitch structure. To follow the complete folding path of the structure, a nonlinear iterative predictor-corrector algorithm based on the Newton method is adopted. First, a simple tetrahedral example of the class of two-orbit structures is presented. Typical configurations along the folding path are shown. Larger members of the class of structures are also presented, all with cubic symmetry. These switch-pitch structures could have useful applications as deployable structures.

Predictive control for spacecraft rendezvous in an elliptical orbit using an FPGA

A field programmable gate array (FPGA)-based predictive controller for a spacecraft rendezvous manoeuvre is presented. A linear time varying prediction model is used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of manoeuvres. The resulting constrained optimisation problems are solved using a primal dual interior point algorithm. The majority of the computational demand is in solving a set of linear equations at each iteration of this algorithm. To accelerate this operation, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft core processor. The system is demonstrated in closed loop by linking the FPGA with a simulation of the plant dynamics running in Simulink on a PC, using Ethernet. © 2013 EUCA.