Analytical Guidance Laws for Aerial Robot Orifice Passage
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing techniques for controlling robotic vehicles to execute precise three-dimensional maneuvers through openings, such as windows or orifices, are limited by the need for numerical integration of dynamic equations, which is computationally intensive and requires frequent recalculations due to changes in the opening's size or position, and often require the vehicle to change speed or come to a halt.
Innovation Solution
A control feedback loop system that uses analytical guidance laws to determine an acceleration vector based on the vehicle's velocity and orientation relative to the opening, allowing the vehicle to pass through without changing speed and without the need for numerical integration, using onboard sensors and kinematic devices like elevator, aileron, and rotor thrust control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical integration of dynamic equations is used to generate reference trajectory, then the vehicle can be guided through the opening, but the computational complexity and time required increase significantly
Solution Approach 1:
The patent replaces the numerical integration method (computational/mechanical approach) with an analytical guidance law based on geometric relationships. Instead of numerically solving differential equations to generate trajectories, the system uses closed-form mathematical expressions that directly compute the required trajectory and control inputs, significantly reducing computational complexity while maintaining precision
Solution Approach 2:
The patent extracts the essential geometric relationships from the complex dynamic equations and formulates a simplified analytical guidance law. By taking out only the critical geometric constraints and relationships needed for trajectory generation, the system avoids the computational burden of full numerical integration while preserving the necessary precision for safe passage through the opening
2Reliability
If numerical integration is performed frequently to account for changes in opening position or size, then the guidance remains accurate, but the computational time and resources increase
Solution Approach 1:
The analytical guidance law replaces repeated numerical integration with closed-form calculations that can be quickly re-evaluated when opening parameters change. The geometric relationships allow for rapid recalculation of trajectories without the computational overhead of numerical methods, maintaining guidance accuracy while reducing recalculation time
Solution Approach 2:
The patent formulates the guidance law in advance using analytical expressions that are ready for immediate evaluation. When the opening position or size changes, the pre-formulated analytical relationships can be quickly re-evaluated with new parameters, avoiding the need to perform time-consuming numerical integration from scratch
3Measurement precision
If the vehicle changes speed or comes to a halt to pass through the opening, then the maneuver precision improves, but the mission time and energy consumption increase
Solution Approach 1:
The analytical guidance law dynamically adjusts the vehicle's trajectory and orientation in real-time based on the geometric relationship with the opening, allowing the vehicle to maintain forward motion while achieving precise passage. The continuous analytical solutions provide smooth control commands that maintain maneuver precision without requiring speed changes or halts
Data Source
AI summary
This document generally describes a safe-passage guidance strategy developed in a relative velocity framework to enable a generic aerial robot execute a precision three-dimensional maneuver through a narrow orifice in a wall. The relative sizes of the robot and the orifice can be such that the orifice is only slightly larger than the robot. The orifice can be approximated as an elliptical shape, and analytical nonlinear guidance laws incorporating state-based switching can be derived. Guidance laws can be used to maneuver the robot through both fixed and moving orifices as well as in scenarios when the orifice is closing with time.