Symbolic Differentiation for Autonomous UAV Path and Camera Control
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Solution Overview
Problem
Existing UAV control systems require constant human intervention to achieve multifaceted goals, such as imaging targets while avoiding regions and optimizing energy consumption, which limits autonomous operation.
Innovation Solution
A UAV system that utilizes cost functions to autonomously control movement, adjusting flight paths and camera angles based on multiple cost functions, including distance, energy, and penalty constraints, using computer-implemented symbolic differentiation and first-order retraction techniques for real-time decision-making.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If human control is used to operate UAV, then control precision is improved, but automation level deteriorates
Solution Approach 1:
The UAV system performs automatic differentiation and computes gradients autonomously through symbolic computation engines, eliminating the need for human operators to manually calculate or adjust control parameters. The system serves itself by automatically generating and applying cost function derivatives for optimization.
Solution Approach 2:
The patent replaces manual human control operations with an automated computational system that uses symbolic mathematics and gradient computation. The mechanical interaction of human operators adjusting controls is substituted with an electronic-symbolic computation system that automatically calculates optimal control inputs.
2Measurement precision
If manual control adjustment is used, then control accuracy is improved, but operation speed deteriorates
Solution Approach 1:
The system pre-computes symbolic derivatives of cost functions and prepares gradient computation templates in advance. By having the differentiation rules and computational structures ready beforehand, the system can rapidly evaluate gradients during operation without performing manual calculations in real-time.
Solution Approach 2:
Manual calculation methods are replaced with automated symbolic computation engines that efficiently evaluate gradients. The computational system substitutes human mathematical operations with algorithmic processing that is both accurate and fast.
3Extent of automation
If symbolic differentiation is implemented, then automation level is improved, but computational complexity worsens
Solution Approach 1:
The computational system divides the differentiation process into discrete, manageable components representing individual cost functions and their derivatives. Each cost function is processed separately, and their gradients are computed and applied in sequence, making the overall complex task manageable through systematic segmentation.
Solution Approach 2:
The symbolic computation engine implements a universal differentiation framework that handles multiple cost functions through a single automated process. The same computational machinery processes different cost functions by applying general differentiation rules, eliminating the need for separate manual analysis of each function.
Data Source
AI summary
A computer accesses an input element storage and an output element storage. The computer accesses a symbolic expression for output element storage as a function of the input element storage. The computer computes, using a symbolic computation engine of the computer, a symbolic expression for the tangent space Jacobian of the output element storage with respect to an input tangent space. The computer outputs the computed expression.