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Safe Control for Soft-Rigid Robots with Self-Contact using Control Barrier Functions

Zach J. Patterson, Wei Xiao, Emily Sologuren, Daniela Rus

TL;DR

This paper investigates the application of Control Barrier Functions and High Order CBFs to manage self-contact scenarios in serially connected soft-rigid hybrid robots and establishes CBFs within a classical control framework for self-contact dynamics.

Abstract

Incorporating both flexible and rigid components in robot designs offers a unique solution to the limitations of traditional rigid robotics by enabling both compliance and strength. This paper explores the challenges and solutions for controlling soft-rigid hybrid robots, particularly addressing the issue of self-contact. Conventional control methods prioritize precise state tracking, inadvertently increasing the system's overall stiffness, which is not always desirable in interactions with the environment or within the robot itself. To address this, we investigate the application of Control Barrier Functions (CBFs) and High Order CBFs to manage self-contact scenarios in serially connected soft-rigid hybrid robots. Through an analysis based on Piecewise Constant Curvature (PCC) kinematics, we establish CBFs within a classical control framework for self-contact dynamics. Our methodology is rigorously evaluated in both simulation environments and physical hardware systems. The findings demonstrate that our proposed control strategy effectively regulates self-contact in soft-rigid hybrid robotic systems, marking a significant advancement in the field of robotics.

Safe Control for Soft-Rigid Robots with Self-Contact using Control Barrier Functions

TL;DR

This paper investigates the application of Control Barrier Functions and High Order CBFs to manage self-contact scenarios in serially connected soft-rigid hybrid robots and establishes CBFs within a classical control framework for self-contact dynamics.

Abstract

Incorporating both flexible and rigid components in robot designs offers a unique solution to the limitations of traditional rigid robotics by enabling both compliance and strength. This paper explores the challenges and solutions for controlling soft-rigid hybrid robots, particularly addressing the issue of self-contact. Conventional control methods prioritize precise state tracking, inadvertently increasing the system's overall stiffness, which is not always desirable in interactions with the environment or within the robot itself. To address this, we investigate the application of Control Barrier Functions (CBFs) and High Order CBFs to manage self-contact scenarios in serially connected soft-rigid hybrid robots. Through an analysis based on Piecewise Constant Curvature (PCC) kinematics, we establish CBFs within a classical control framework for self-contact dynamics. Our methodology is rigorously evaluated in both simulation environments and physical hardware systems. The findings demonstrate that our proposed control strategy effectively regulates self-contact in soft-rigid hybrid robotic systems, marking a significant advancement in the field of robotics.
Paper Structure (11 sections, 1 theorem, 19 equations, 6 figures)

This paper contains 11 sections, 1 theorem, 19 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and System Formulation
  3. High Order CBFs
  4. Kinematics and Dynamics
  5. CBFs for Soft Robots
  6. Control Approach
  7. Nominal Control Input
  8. CBFs for Safe Self-contact
  9. Simulation Results
  10. Hardware Results
  11. Discussion and Conclusion

Key Result

Theorem 1

Given a HOCBF $b(\bm x)$ from Def. def:hocbf with the associated sets $C_{1}, \dots, C_{m}$ defined by (eqn:sets), if $\bm x(0) \in C_{1} \cap,\dots,\cap C_{m}$, then any Lipschitz continuous controller $\bm u(t)\in U$ that satisfies the constraint in (eqn:constraint), $\forall t\geq0$ renders $C_{1

Figures (6)

  • Figure 1: An example of the type of hardware we examine for this work, where the modular soft-rigid segments frequently make self contact. We seek to operationalize representations of distance functions such as $c_j$ to gracefully control such structures in the presence of self contact using CBFs.
  • Figure 2: Illustration of some key quantities for the robot. The six red dots corresponding to the corners of the plate are used as our CBFs by deriving the forward kinematics of each point. The quantity $d$ represents the distance to these corners, $\phi$ represents the angle of rotation for the vector pointing to each corner from the center.
  • Figure 3: Results in Simulation. a) Shows the generalized coordinates (solid lines) and set points (dashed lines) for a two segment simulated soft-rigid manipulator. b) Output torques from QP (\ref{['eq:qp']}). c) Safety constraint values during the simulation. Note that there are 6 safety constraint functions (\ref{['eq:b']}) per segment for a total of 12 (lines corresponding to the first and second segment are solid and dashed respectively).
  • Figure 4: Plots for experiments on hardware. a) Generalized coordinates and set points for two segment manipulator controlled with a CBF. b) Commanded generalized forces from Eq. (\ref{['eq:qp']}). c) Safety constraint values during an experiment. Note that there are 6 functions per segment for a total of 12. Note that the barrier functions are prevented from dropping below zero. d) Generalized coordinates and set points for two segment manipulator controlled with PD+. e) Commanded generalized forces from Eq. (\ref{['eq:nom']}). f) Safety constraints (which are not actually enforced by the nominal controller and thus are allowed to be violated).
  • Figure 5: Top: snapshots from trials controlled by QP (\ref{['eq:qp']}). Bottom: snapshots from PD+ controlled trial
  • ...and 1 more figures

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1: Xiao2019