Symbolic Jacobian Chain Rule for Real-Time UAV Control
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Solution Overview
Problem
Current UAV systems require constant human intervention for autonomous flight, especially to ensure sufficient battery power for return to base station, and manual symbolic differentiation is cumbersome and error-prone, especially under time constraints.
Innovation Solution
A flight control subsystem on the UAV accesses cost functions to autonomously control movement, adjusting them based on user input or conflicts, and employs multithreaded processing for parallel symbolic differentiation to optimize flight paths and camera angles in real-time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If manual symbolic differentiation is used for real-time UAV control optimization, then implementation simplicity is maintained, but computation speed and accuracy deteriorate due to time constraints and error-proneness
Solution Approach 1:
The patent pre-computes symbolic derivatives of cost functions offline and stores them in a database. During real-time UAV operation, the system retrieves pre-computed derivatives instead of computing them on-the-fly, dramatically reducing computation time while maintaining accuracy and eliminating manual differentiation errors.
Solution Approach 2:
The system creates symbolic representations of cost functions and their derivatives in a formal language, then generates optimized code copies from these symbolic templates. This allows the UAV to execute efficient pre-processed control algorithms rather than performing complex symbolic manipulation during flight.
2Adaptability or versatility
If autonomous operation with multiple cost function optimization is implemented, then operational versatility improves, but computational complexity and processing requirements worsen
Solution Approach 1:
The patent divides the control problem into separate cost functions, each representing a specific operational objective (e.g., imaging quality, battery conservation, navigation). Each cost function is independently optimized with its own pre-computed derivatives, allowing the UAV to handle multiple objectives without overwhelming computational complexity.
Solution Approach 2:
The system implements a universal optimization framework that can handle any number of cost functions through a standardized process: define cost function, retrieve pre-computed derivatives, and optimize. This multi-functional approach allows the UAV to adapt to various operational scenarios (imaging, navigation, battery management) using the same computational infrastructure.
3Measurement precision
If real-time symbolic differentiation is performed during UAV flight, then control optimization accuracy improves, but computation time and energy consumption worsen
Solution Approach 1:
The system performs all symbolic differentiation and derivative computation offline before flight, storing results in a database. During real-time operation, the UAV simply retrieves pre-computed derivatives, achieving both high accuracy (through symbolic methods) and fast computation (through lookup operations).
Solution Approach 2:
The system dynamically switches between offline symbolic computation mode (for accuracy) and online retrieval mode (for speed). This dynamic approach allows the UAV to benefit from the precision of symbolic differentiation without suffering from its computational time requirements during actual flight.
Data Source
AI summary
A computer accesses a first symbolic expression for an output value as a function of an input value. The computer computes a first symbolic Jacobian of the input value with respect to an input tangent space from a symbolic Lie group definition. The computer computes a second symbolic Jacobian of the output value with respect to the input value. The computer computes a third symbolic Jacobian of an output tangent space with respect to the input value from the symbolic Lie group definition. The computer applies symbolic matrix multiplication to the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space. The computer provides a representation of the second symbolic expression.