Vehicle Motion Control With Geometric Algebra Error Modeling
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Solution Overview
Problem
Current vehicle control systems, particularly for drones, face limitations in maintaining a consistent error or noise model, which hinders their ability to accurately navigate and respond to environmental changes, especially in complex environments without GPS signals, due to non-unified spatial representations and inadequate error estimation.
Innovation Solution
The implementation of geometric algebra provides a unified representation of space across all sensors and systems, enabling coherent integration of flight and sensor data, allowing for consistent error and noise modeling, and enabling the drone to differentiate between wind and wall confrontations through 'Stick Integration' and 'Empathy Modeling', thereby improving navigation and stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional control systems are used for drones, then basic flight control is achieved, but consistent error and noise modeling cannot be maintained throughout the system
Solution Approach 1:
The control system is segmented into multiple independent modules, each maintaining its own error and noise models. This allows consistent error modeling across the entire system while keeping each module's complexity manageable. The segmentation enables parallel processing of error estimation without creating a single complex centralized system.
Solution Approach 2:
The patent introduces a new dimension of error representation by modeling errors and noise in multiple frames of reference simultaneously. This dimensional approach allows the system to maintain consistent error models across different coordinate systems without increasing the fundamental complexity of the control architecture.
2Measurement precision
If non-unified spatial representations are used, then implementation is simpler, but accurate navigation and error estimation are hindered
Solution Approach 1:
The patent implements a unified spatial representation system that serves multiple functions simultaneously: it provides accurate error estimation, enables navigation in complex environments, and maintains consistency across different sensor frames of reference. This universal system replaces multiple separate spatial representations, improving precision without proportionally increasing complexity.
Solution Approach 2:
The unified spatial representation acts as an intermediary layer between different sensors and the control system. It mediates the transformation and coordination of data from multiple sources, enabling accurate error estimation while simplifying the overall system architecture through a single coherent framework.
3Reliability
If GPS signals are available, then navigation accuracy is improved, but stable flight in GPS-denied environments cannot be achieved
Solution Approach 1:
The system performs preliminary error modeling and spatial representation setup before GPS signals become unavailable. By establishing accurate error models and unified spatial frameworks in advance, the drone maintains navigation precision and flight stability even when GPS signals are denied, as the pre-configured systems continue to function without external assistance.
Data Source
AI summary
A method and system for controlling movement of a vehicle. Movement, orientation, and position data of the vehicle is collected. A model of kinematics of the vehicle and its environment is created and a Theory of World model is produced and updated. The model includes geometric algebra multivectors. Errors and noise are stored as geometrically meaningful first-class objects within the multivectors. Geometric algebra operations are used to manipulate the model during operation. Error and noise data are propagated and manipulated using geometric algebra operations to reflect measurement and processing errors or noise. The models are used in generation of control data with a primary intent of ensuring stability. Operations such as intersections are used to compare position, orientation, and movement of the vehicle against position, orientation, and movement of objects in its environment. System tasks include, but are not limited to, kinematics, inverse kinematics, collision avoidance, and dynamics.