Spacecraft Orbit Transfer Using Equinoctial Control-Lyapunov Feedback
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Solution Overview
Problem
Conventional orbit transfer methods using chemical propulsion require intense and short thrusts, while electric propulsion systems with continuous or quasi-continuous thrust face challenges in controlling thrust intensity and orientation, leading to instability and inefficiency, especially in managing longitude encounter constraints and orbits with low eccentricity and inclination.
Innovation Solution
A closed-loop control method using a heuristic control law based on a Control-Lyapunov function expressed in equinoctial orbital parameters, averaged over at least one half-period, to compute and apply thrust control in real-time, leveraging GNSS measurements and an embedded processor for stable and optimal orbit transfer.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If open-loop control with pre-computed optimal control law is used, then transfer duration and propellant consumption are optimized, but the spacecraft trajectory deviates significantly between updates increasing transfer duration and propellant consumption
Solution Approach 1:
The patent implements a closed-loop feedback control system where the control law is continuously updated based on real-time measurements of the spacecraft's position and velocity. The feedback mechanism compares the actual trajectory with the desired trajectory and adjusts the thrust vector accordingly, preventing significant deviations between control updates while maintaining transfer efficiency.
Solution Approach 2:
The control system dynamically adapts the optimal control law by recomputing it at regular intervals using the current state of the spacecraft. This dynamic update approach allows the system to maintain optimality while responding to trajectory deviations, balancing computational efficiency with real-time adaptability.
2Ease of operation
If stabilization heuristics type techniques (Q-Law) are used, then control implementation is simplified, but instability occurs in orbits with low eccentricity and low inclination
Solution Approach 1:
The patent transforms the control problem by changing the parameter representation from conventional orbital elements to equinoctial orbital parameters. This parameter transformation eliminates the singularities that occur in traditional orbital elements when eccentricity or inclination approaches zero, providing a stable and continuous control law across all orbital conditions while maintaining implementation simplicity.
3Adaptability or versatility
If conventional orbital parameters are used in control law, then standard orbital mechanics apply, but singularities occur in orbits with low eccentricity and low inclination
Solution Approach 1:
The patent employs equinoctial orbital parameters instead of conventional orbital elements (such as right ascension of ascending node and argument of perigee) that become singular when inclination or eccentricity is zero. The equinoctial parameters provide a non-singular representation that remains valid and differentiable for all orbital conditions, enabling stable control law computation throughout the transfer.
Data Source
AI summary
An orbit transfer method for a spacecraft using a continuous or quasi-continuous thrust propulsion, the method comprises: the acquisition, at least once in each half-revolution of the spacecraft, of measurements of its position and of its velocity; the computation of a thrust control function as a function of the measurements; and the driving of the thrust in accordance with the control law; wherein the control law is obtained from a Control-Lyapunov function using orbital parameters, preferably equinoctial, of the spacecraft, averaged over at least one half-revolution. An embedded driving system for a spacecraft for implementing such a method and a spacecraft equipped with the driving system are provided.