Spacecraft Formation MPC Using Virtual Point Polytope Boundaries
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Solution Overview
Problem
Spacecraft formation maneuvers are complicated by the need to maintain formation while minimizing fuel consumption, constrained by limited communication bandwidth and computing resources, which complicates autonomous calculations for multiple spacecraft.
Innovation Solution
The method employs model predictive control (MPC) with virtual points and polytope boundaries to simplify calculations, allowing spacecraft to autonomously perform maneuvers within defined boundaries, reducing fuel consumption and improving computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of energy
If traditional formation control methods are used to maintain spacecraft formation, then formation stability is maintained, but fuel consumption increases and computational complexity increases
Solution Approach 1:
The patent divides the formation control problem into independent polytope boundary calculations for each spacecraft relative to a virtual point. Each spacecraft's control is optimized independently within its own polytope boundary, segmenting the complex multi-spacecraft coordination problem into simpler individual optimization problems that reduce overall computational complexity and fuel consumption.
Solution Approach 2:
The patent introduces a virtual point as an intermediary that represents the collective formation state. Instead of directly controlling relative positions between all pairs of spacecraft, the virtual point serves as a mediator that simplifies the control architecture, allowing each spacecraft to be controlled relative to this single virtual reference point rather than requiring complex inter-spacecraft coordination.
2Productivity
If autonomous maneuvering is implemented for spacecraft formation, then control efficiency improves, but communication bandwidth requirements increase and calculation complexity increases
Solution Approach 1:
The patent enables autonomous maneuvering where each spacecraft independently calculates its own control inputs based on its current state and the polytope boundary constraints. The spacecraft perform self-service by executing maneuvers without requiring continuous ground station intervention or complex real-time communication, thereby improving control efficiency while reducing communication bandwidth requirements.
3Loss of energy
If polytope boundaries are used to constrain spacecraft maneuvers, then fuel consumption is minimized, but the complexity of defining and maintaining boundaries increases
Solution Approach 1:
The patent creates a symmetric polytope boundary structure where all spacecraft are treated equally with identical boundary constraints relative to the virtual point. This equipotential approach simplifies the boundary definition process by applying the same geometric constraints uniformly across all spacecraft, reducing the complexity of defining and maintaining boundaries while ensuring optimal fuel-efficient maneuvers within each polytope.
Data Source
AI summary
For model predictive control for a spacecraft formation, a method calculates a virtual point that represents a plurality of spacecraft orbiting in a spacecraft formation. The method calculates an outer polytope boundary and an inner polytope boundary relative to the virtual point for a given spacecraft of the plurality of spacecraft. The method maneuvers the given spacecraft to within the inner polytope boundary using model predictive control (MPC) to minimize fuel consumption.