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Towards a Theory of Control Architecture: A quantitative framework for layered multi-rate control

Nikolai Matni, Aaron D. Ames, John C. Doyle

TL;DR

The paper articulates a universal theory of layered control architectures (LCAs) to analyze and design complex, multi-rate systems spanning engineered and natural domains. It proposes a quantitative framework that derives LCAs from a global synthesis problem via problem decomposition and inter-layer relaxations, yielding three-layer structures (decision making, trajectory planning, feedback control) and aligning with model-based planning (MPC) and real-time control strategies. It further explores robotic instantiations, multi-rate architectures, safe navigation/locomotion, and learning, and introduces a multi-criterion optimization view with diversity-enabled sweet spots (DeSS) to guide architecture design. A case study in sensorimotor control links delays, quantization, and neural signaling to DeSS, while extensive experiments, visuals, and analogies across clothing, Lego, and bacteria illustrate the universality. The work advocates formal design tools (Pareto efficiency, Lyapunov/CBF safety, and data-driven modeling) to enable scalable, safe, and adaptable LCAs in robotics, automation, and biology, aiming for a principled theory of end-to-end control stacks.

Abstract

This paper focuses on the need for a rigorous theory of layered control architectures (LCAs) for complex engineered and natural systems, such as power systems, communication networks, autonomous robotics, bacteria, and human sensorimotor control. All deliver extraordinary capabilities, but they lack a coherent theory of analysis and design, partly due to the diverse domains across which LCAs can be found. In contrast, there is a core universal set of control concepts and theory that applies very broadly and accommodates necessary domain-specific specializations. However, control methods are typically used only to design algorithms in components within a larger system designed by others, typically with minimal or no theory. This points towards a need for natural but large extensions of robust performance from control to the full decision and control stack. It is encouraging that the successes of extant architectures from bacteria to the Internet are due to strikingly universal mechanisms and design patterns. This is largely due to convergent evolution by natural selection and not intelligent design, particularly when compared with the sophisticated design of components. Our aim here is to describe the universals of architecture and sketch tentative paths towards a useful design theory.

Towards a Theory of Control Architecture: A quantitative framework for layered multi-rate control

TL;DR

The paper articulates a universal theory of layered control architectures (LCAs) to analyze and design complex, multi-rate systems spanning engineered and natural domains. It proposes a quantitative framework that derives LCAs from a global synthesis problem via problem decomposition and inter-layer relaxations, yielding three-layer structures (decision making, trajectory planning, feedback control) and aligning with model-based planning (MPC) and real-time control strategies. It further explores robotic instantiations, multi-rate architectures, safe navigation/locomotion, and learning, and introduces a multi-criterion optimization view with diversity-enabled sweet spots (DeSS) to guide architecture design. A case study in sensorimotor control links delays, quantization, and neural signaling to DeSS, while extensive experiments, visuals, and analogies across clothing, Lego, and bacteria illustrate the universality. The work advocates formal design tools (Pareto efficiency, Lyapunov/CBF safety, and data-driven modeling) to enable scalable, safe, and adaptable LCAs in robotics, automation, and biology, aiming for a principled theory of end-to-end control stacks.

Abstract

This paper focuses on the need for a rigorous theory of layered control architectures (LCAs) for complex engineered and natural systems, such as power systems, communication networks, autonomous robotics, bacteria, and human sensorimotor control. All deliver extraordinary capabilities, but they lack a coherent theory of analysis and design, partly due to the diverse domains across which LCAs can be found. In contrast, there is a core universal set of control concepts and theory that applies very broadly and accommodates necessary domain-specific specializations. However, control methods are typically used only to design algorithms in components within a larger system designed by others, typically with minimal or no theory. This points towards a need for natural but large extensions of robust performance from control to the full decision and control stack. It is encouraging that the successes of extant architectures from bacteria to the Internet are due to strikingly universal mechanisms and design patterns. This is largely due to convergent evolution by natural selection and not intelligent design, particularly when compared with the sophisticated design of components. Our aim here is to describe the universals of architecture and sketch tentative paths towards a useful design theory.
Paper Structure (67 sections, 3 theorems, 77 equations, 15 figures, 1 table)

This paper contains 67 sections, 3 theorems, 77 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. A model LCA
  3. A brief overview of control architecture research
  4. Paper organization
  5. Part 1.1: Layered Control Architectures via Optimal Control Decomposition
  6. Notation
  7. The overall synthesis problem
  8. Layering via Problem Decomposition and Relaxation
  9. Decision making layer
  10. Trajectory planning layer
  11. Real-time feedback control layer
  12. Discussion
  13. What about the hardware?
  14. How many layers should there be?
  15. Multi-rate control
  16. ...and 52 more sections

Key Result

Theorem 1

Consider a control system eqn:affinecontrolsys, where $x = (q,\dot{q})$, and a safe set $\mathcal{S} = \{ q \in Q : h(q) \geq 0\}$. Assume that $h$ has bounded gradient, i.e., there exists $K_h>0$ s.t. ${\left\| \frac{\partial h}{\partial q}\right\|}_2 \leq K_h$ for all $q \in \mathcal{S}$. Let $v_{ where

Figures (15)

  • Figure 1: Figure taken from apollo, showing the GNC architecture used for Apollo missions.
  • Figure 2: Layered control architectures are ubiquitous across natural and engineered systems. We seek to initiate a quantitative study of layered control architectures based on the illustrated three-layer abstraction.
  • Figure 3: A mobile robot (the Gritbot) modeled as a Dubins' car. In this case, the Gritbot that is deployed in the Robotarium which utilizes a LCA to allow for the implementation of user algorithms in a safe fashion pickem2017robotarium.
  • Figure 4: Moving from continuous (left) to discrete (right) state space in the robot navigation running example. We see that due to the resolution of the partition, the set of discrete states $\mathcal{S}_1$ is an under-approximation of the corresponding first objective set $\mathcal{X}_1$. The blue circles illustrate the discrete state space trace defined by the decision making layer; the red arrow shows the reference trajectory generated by the planning layer using the blue circles as waypoint constraints; the black dashed line is the actual system evolution, as driven by the feedback control layer on the continuous time dynamics.
  • Figure 5: Multi-rate robotic control can be viewed through the lens of layered architectures (figure from rosolia2022unified).
  • ...and 10 more figures

Theorems & Definitions (10)

  • Example 1: Running example: robot navigation
  • Example 2: Running example: robot navigation
  • Example 3: Running example: robot navigation
  • Example 4: Running example: robot navigation
  • Example 5: Running example: robot navigation
  • Example 6: Running example: robot navigation
  • Theorem 1
  • Example 7: Running example: robot navigation
  • Theorem 2
  • Theorem 3