Tangent-Space Jacobian Computation for Symbolic Matrix Differentiation
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Solution Overview
Problem
Existing UAV control systems require human intervention to navigate and ensure sufficient battery power, limiting their autonomous operation and efficiency.
Innovation Solution
A flight control subsystem on the UAV accesses a problem definition including cost functions associated with its travel, allowing it to automatically determine flight paths, tilts, and camera angles based on optimized cost function adjustments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If human intervention is used to control UAV navigation and battery management, then control reliability is improved, but extent of automation deteriorates
Solution Approach 1:
The UAV control system automatically monitors battery power levels and adjusts flight parameters without human intervention. The system self-manages navigation decisions, battery management, and flight parameter optimization through autonomous algorithms that process sensor data and execute control actions independently.
Solution Approach 2:
The system continuously monitors flight parameters, battery status, and environmental conditions, then uses this feedback to automatically adjust navigation paths and control inputs. The feedback loop enables the UAV to adapt its behavior in real-time based on actual system state and mission requirements.
2Adaptability or versatility
If multiple cost functions are considered for UAV operation, then adaptability is improved, but device complexity increases
Solution Approach 1:
The control system segments the complex control problem into multiple independent cost functions, each handling a specific aspect of flight optimization (e.g., navigation, battery management, obstacle avoidance). This modular approach allows each cost function to be developed, tuned, and executed independently while contributing to the overall optimized control decision.
3Extent of automation
If automatic operation is implemented without human control, then extent of automation is improved, but control reliability may deteriorate
Solution Approach 1:
The UAV control system automatically monitors battery power levels and adjusts flight parameters without human intervention. The system self-manages navigation decisions, battery management, and flight parameter optimization through autonomous algorithms that process sensor data and execute control actions independently.
Solution Approach 2:
The system continuously monitors flight parameters, battery status, and environmental conditions, then uses this feedback to automatically adjust navigation paths and control inputs. The feedback loop enables the UAV to adapt its behavior in real-time based on actual system state and mission requirements.
Data Source
AI summary
A computer accesses a first symbolic expression for an output matrix as a function of an input matrix at a computing device comprising processing circuitry and memory. The computer computes a first Jacobian of the input matrix with respect to an input tangent space. The computer computes a second Jacobian of the output matrix with respect to the input matrix. The computer computes a third Jacobian of an output tangent space with respect to the input matrix. The computer applies symbolic matrix multiplication to the first Jacobian, the second Jacobian, and the third 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, the second symbolic expression representing a computed tangent-space Jacobian.