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Necessary and Sufficient Conditions for Input-Output Extension in Underactuated Nonlinear Systems

Core Concepts
The author addresses the problem of extending the output capability of underactuated systems by adding supplementary inputs while keeping the internal controller unmodified.
The content discusses the challenges and solutions related to re-targeting commercial under-actuated robotic systems for higher-dimensional tasks. Necessary and sufficient conditions are derived to extend controlled outputs by introducing additional inputs while maintaining the original internal controller. The paper presents examples from robotics, such as aerial physical interaction tasks with quadrotors. The study reveals a methodology to augment system capabilities through input-output extension, showcasing practical value in studying underactuated systems.
Commercial platforms have low-level internal controllers controlling a subset of system degrees-of-freedom. Necessary and sufficient conditions are derived for extending controlled outputs by adding extra inputs. Aerial Physical Interaction tasks require full pose control, posing challenges due to under-actuation. Internal controllers stabilize tool operations for quadrotors with unstable dynamics. Proposed methodology involves supplying additional inputs to work cohesively with existing virtual inputs.
"We propose to tackle the problem by supplying the system with additional inputs that act cohesively together with the virtual inputs provided by the system’s original low-level closed controller." "Our primary objective is to augment these systems by introducing supplementary inputs, attaining increased output capability." "The complexity of APhI with an UA quadrotor led the aerial robotics community to propose more complex designs of fully actuated aerial robots."

Deeper Inquiries

How can this methodology be applied to other types of underactuated systems beyond robotics?

The methodology presented in the context can be extended to various underactuated systems beyond robotics, such as marine vehicles, autonomous cars, or even industrial automation. By identifying the internal controller structure and its limitations within a system, additional inputs can be strategically introduced to enhance the output capabilities without modifying the existing control architecture significantly. This approach is particularly useful in scenarios where commercial platforms come with closed-source controllers that cannot be altered but need to perform tasks requiring higher-dimensional outputs.

What are potential drawbacks or limitations of extending input-output capabilities in internally controlled systems?

While extending input-output capabilities in internally controlled systems offers significant advantages in enhancing performance and achieving more complex tasks, there are some drawbacks and limitations to consider: Increased Complexity: Adding supplementary inputs may introduce complexity into the system's control framework, making it harder to analyze and tune. Compatibility Issues: Ensuring seamless integration between additional inputs and existing controls can be challenging and may lead to compatibility issues. Controller Saturation: The introduction of extra inputs could potentially saturate the internal controller if not carefully managed, leading to instability or suboptimal performance. System Identification: Proper identification of system dynamics becomes crucial when adding new inputs, as inaccuracies could affect overall system behavior.

How does this research impact advancements in autonomous systems beyond aerial robotics?

This research has broader implications for advancements in autonomous systems across various domains beyond aerial robotics: Enhanced Autonomy: By enabling underactuated systems with increased output capability through additional inputs while keeping internal controllers intact, autonomy levels can be improved. Versatility: The ability to extend input-output capabilities allows for greater versatility in performing diverse tasks efficiently without major modifications. Efficiency Improvement: With a methodical approach like this one, autonomous systems can achieve better efficiency by leveraging both virtual references from internal controllers and supplemental inputs effectively. Safety Considerations: Advancements stemming from this research contribute towards developing safer autonomous systems capable of handling more complex operations reliably. By applying these principles outside aerial robotics contexts, such as self-driving cars or underwater vehicles, researchers can push boundaries on what autonomous systems are capable of achieving while maintaining stability and reliability essential for real-world applications.