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Validation of Space Robotics in Underwater Environments via Disturbance Robustness Equivalency

Joris Verhagen, Elias Krantz, Chelsea Sidrane, David Dörner, Nicola De Carli, Pedro Roque, Huina Mao, Gunnar Tibert, Ivan Stenius, Christer Fuglesang, Dimos Dimarogonas, Jana Tumova

Abstract

We present an experimental validation framework for space robotics that leverages underwater environments to approximate microgravity dynamics. While neutral buoyancy conditions make underwater robotics an excellent platform for space robotics validation, there are still dynamical and environmental differences that need to be overcome. Given a high-level space mission specification, expressed in terms of a Signal Temporal Logic specification, we overcome these differences via the notion of maximal disturbance robustness of the mission. We formulate the motion planning problem such that the original space mission and the validation mission achieve the same disturbance robustness degree. The validation platform then executes its mission plan using a near-identical control strategy to the space mission where the closed-loop controller considers the spacecraft dynamics. Evaluating our validation framework relies on estimating disturbances during execution and comparing them to the disturbance robustness degree, providing practical evidence of operation in the space environment. Our evaluation features a dual-experiment setup: an underwater robot operating under near-neutral buoyancy conditions to validate the planning and control strategy of either an experimental planar spacecraft platform or a CubeSat in a high-fidelity space dynamics simulator.

Validation of Space Robotics in Underwater Environments via Disturbance Robustness Equivalency

Abstract

We present an experimental validation framework for space robotics that leverages underwater environments to approximate microgravity dynamics. While neutral buoyancy conditions make underwater robotics an excellent platform for space robotics validation, there are still dynamical and environmental differences that need to be overcome. Given a high-level space mission specification, expressed in terms of a Signal Temporal Logic specification, we overcome these differences via the notion of maximal disturbance robustness of the mission. We formulate the motion planning problem such that the original space mission and the validation mission achieve the same disturbance robustness degree. The validation platform then executes its mission plan using a near-identical control strategy to the space mission where the closed-loop controller considers the spacecraft dynamics. Evaluating our validation framework relies on estimating disturbances during execution and comparing them to the disturbance robustness degree, providing practical evidence of operation in the space environment. Our evaluation features a dual-experiment setup: an underwater robot operating under near-neutral buoyancy conditions to validate the planning and control strategy of either an experimental planar spacecraft platform or a CubeSat in a high-fidelity space dynamics simulator.
Paper Structure (21 sections, 19 equations, 5 figures, 1 table)

This paper contains 21 sections, 19 equations, 5 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Signal Temporal Logic
  4. PROBLEM STATEMENT
  5. Models
  6. PLANNING
  7. Disturbance Robustness as a Metric
  8. Space Plan Synthesis
  9. Underwater Plan Synthesis
  10. CONTROL
  11. Disturbance Estimation
  12. Space robot MPC
  13. Dynamical Equivalency
  14. Underwater robot MPC
  15. VALIDATION
  16. ...and 6 more sections

Figures (5)

  • Figure 1: A physical BlueROV underwater robot is utilized to validate a planner and controller which aim to inspect a passive target in space. While the environments are distinct, they share sufficient similarities in order to be used as a validation platform.
  • Figure 2: Hardware results of the Feedback-Equivalent underwater-robot MPC of \ref{['eq:mpc_uw']} on the BlueROV. (a): time-stamped images from the experiment, (b) planned and executed trajectory, (c) position and the maximal spatial deviation $\delta_{\phi_{uw}}=0.11 \leq \rho_{\phi_{uw}} = 0.25$ (indicating satisfaction of $\phi_{uw}$), (d) commanded force and torque with its actuation limits in dotted lines, (e) attitude, (f) estimated force and torque disturbance $\hat{\bm{d}}_{uw}$ with the admissible disturbance bounds $\alpha^*\mathcal{D}_{uw}$. The observed disturbances again being bounded by the disturbance robustness degree $\alpha^*\mathcal{D}_{uw}$ with a satisfied specification provides experimental evidence of operation in the space environment, shown in \ref{['fig:2D-atmos']}.
  • Figure 3: Simulation results of the space-robot MPC of \ref{['eq:mpc_sp']} on ATMOS. (a): time-stamped images from the experiment, (b) planned and executed trajectory in the 2D plane, (c) position and the maximal spatial deviation $\delta_{\phi_{sp}}=0.10 \leq \rho_{\phi_{sp}}=0.25$ (indicating satisfaction of $\phi_{sp}$), (d) commanded force and torque with its actuation limits in dotted lines, (e) attitude, (f) estimated force and torque disturbances $\hat{d}_{sp}$ with the admissible disturbance bounds $\alpha^*\mathcal{D}_{sp}$. The experimental evidence of the underwater validation experiment is translated to the space platform as long as the estimated force and torque disturbances acting on the CubeSat are within the admissible disturbance bounds $\alpha^*\mathcal{D}_{sp}$ which is shown in (f).
  • Figure 4: Hardware results of the Feedback-Equivalent CubeSat MPC of \ref{['eq:mpc_uw']} on the BlueROV. (a): time-stamped images from the experiment, (b) planned and executed trajectory in the 2D plane, (c) position and the maximal spatial deviation $\delta_{\phi_{uw}}=0.13 \leq \rho_{\phi_{uw}}=0.19$ (indicating satisfaction of $\phi_{uw}$), (d) commanded force and torque with its actuation limits in dotted lines, (e) attitude, (f) estimated force and torque disturbances $\hat{d}_{uw}$ with the admissible disturbance bounds $\alpha^*\mathcal{D}_{uw}$. The observed disturbances again being bounded by the disturbance robustness degree $\alpha^*\mathcal{D}_{uw}$ with a satisfied specification provides experimental evidence of operation in the space environment, shown in \ref{['fig:3D-atmos']}.
  • Figure 5: Simulation results of the CubeSat MPC of \ref{['eq:mpc_sp']} on the CubeSat. (a): time-stamped images from the experiment, (b) planned and executed trajectory in the 2D plane, (c) position and the maximal spatial deviation $\delta_{\phi_{sp}}=0.05 \leq \rho_{\phi_{sp}}=0.19$ (indicating satisfaction of $\phi_{sp}$), (d) commanded force and torque with its actuation limits in dotted lines, (e) attitude, (f) estimated force and torque disturbances $\hat{d}_{sp}$ with the admissible disturbance bounds $\alpha^*\mathcal{D}_{sp}$. The experimental evidence of the underwater validation experiment is translated to the space platform as long as the estimated force and torque disturbances acting on the CubeSat are within the admissible disturbance bounds $\alpha^*\mathcal{D}_{sp}$, shown in (f).

Theorems & Definitions (1)

  • Definition 1: Time-bounded STL