ekal2021online

Online Information-Aware Motion Planning with Inertial Parameter Learning for Robotic Free-Flyers

Authors: Ekal, Albee, Coltin, Ventura, Linares, Miller · Year: 2021 · Venue: IEEE (free-flyer / Astrobee robotics; arXiv companion 1906.02758 for prior work)
Raw: md

Summary

This paper introduces RATTLE (Real-time information-Aware Targeted Trajectory planning for Learning via Estimation), an online motion-planning framework that lets a robotic free-flyer (NASA’s Astrobee) deliberately inject excitation into its trajectories to learn uncertain inertial parameters (mass, center-of-mass offset, moment of inertia) en route, instead of pausing for a dedicated system-identification maneuver. The architecture is a four-layer stack: a kinodynamic-RRT global planner, a Fisher-information-aware receding-horizon local planner with a tunable weight γ, a nonlinear MPC controller, and an EKF parameter estimator, all sharing an online-updatable model. It is validated in a high-fidelity 3-DOF Astrobee simulation and in a granite-table hardware proof of concept, showing that information-aware planning reduces the variance of hard-to-observe parameters (notably I_zz).

Key Claims

• An adjustable scalar weight γ on the A-optimality criterion tr(F⁻¹) lets the operator trade off state/fuel cost against parameter information gain inside the same local optimization, so excitation is added only “as much as desired” alongside goal-achieving motion.
• Hardware testing showed I_zz estimate covariance dropped by 25.01% (no payload) and 38.05% (with payload) under information-aware vs. nominal planning, while mass covariance changed little (+2.47% / −3.71%), because nominal translational maneuvers already excite mass but not rotation.
• Center-of-mass offset (c_x, c_y) remained poorly estimated in both informed and uninformed cases due to poor observability.
• Astrobee’s severe actuation limit (u_max ≤ 0.4 N) makes accurate inertial parameters safety-critical before maneuvering with a grappled payload.
• Global kino-RRT plans (~2 m, ~30% obstacle density) solved in 3.59 ± 3.63 s in C++ alongside the full autonomy stack; typical runtimes were below 0.5 s, supporting online replanning.
• Claimed to be the first parametric information-aware planning algorithm with online uncertainty reduction by parameter learning demonstrated for robotic free-flyers, including on hardware.

Method

The system has state x ∈ ℝⁿ, input u ∈ ℝᵐ, uncertain parameters θ ∈ ℝʲ, with stochastic dynamics and measurement models (Eqs. 1–2):

x˙ = f(x, u, θ) + w_x, ỹ = h(x, u, θ) + w_y,

with w_x ~ 𝒩(0, Σ_Q), w_y ~ 𝒩(0, Σ_R), and prior θ₀ ~ 𝒩(θ̂₀, Σ_{θ,0}). The objective (Eq. 3) is a standard terminal-plus-running cost minimized subject to X_free and U.

Regime — free-FLYING. This is unambiguously a free-flying (fully-actuated 6-DOF base) regime, not free-floating: Astrobee actively propels itself via impellers and 12 nozzles, with no reliance on momentum conservation or a reaction-null-space. The rigid-body model (Eq. 4) is written in a body frame not coincident with the CM, so a CM offset c appears explicitly:

[F; τ_{CM0}] = [[m I₃, −m[c]×]; [−m[c]×, I_CM − m[c]×[c]×]] [v˙; ω˙] + [m[w]×[w]× c; [w]× (I_CM − m[c]×[c]_×) ω].

(Note: the second forcing term’s leading factor is printed as [w]× rather than [ω]×, an apparent OCR/typo; physically it is the gyroscopic ω×(I·ω)-type term.) The 3-DOF granite-table reduction (Eqs. 5–7) gives F_x = m[v˙_x − ω˙_z c_y − ω_z² c_x], F_y = m[v˙_y + ω˙z c_x − ω_z² c_y], τ{z0} = m c_x v˙_y − m c_y v˙_x + [I_zz,CM + m(c_y² + c_x²)] ω˙_z, compactly F = [M]x˙ + [C]x (Eq. 8). The estimated parameter vector is θ = {m, c_x, c_y, I_zz}.

Information metric. With θ_{k+1} = θ_k (no parameter process noise), Gaussian measurement noise, and a linear measurement model, the Fisher Information Matrix is F = Σ_{k=0}^N H(t_k)ᵀ Σ⁻¹ H(t_k) (Eq. 9), with sensitivity H(t_k) = ∂h/∂θ + (∂h/∂x)(∂x/∂θ) (Eq. 10). The local planner solves (Eq. 11): minimize Σ_{k=0}^{N−1} xᵀQx + uᵀRu + γ·tr(F⁻¹) subject to the discretized dynamics x_{t+k+1} = f(x_{t+k}, u_{t+k}), x ∈ X_free, u ∈ U, with Q ≻ 0, R ≻ 0. tr(F⁻¹) is the A-optimality criterion (minimizing the parameter uncertainty-ellipsoid axis lengths).

Stack. Global = kino-RRT (motion primitives, ellipsoidal collision checks). Local = ACADO NLP, replan period 12 s, exponentially decaying γ with τ = 1/10 the global horizon. Low-level = NMPC at 10 Hz solving Eq. 11 with γ = 0. Estimator = EKF fed poses/twists plus applied forces/torques; model updates pushed to planner/controller every 16 s to avoid transient-driven instability. Hardware mid-level planner ran onboard at 3 Hz.

Relevance to thesis

RATTLE is a direct architectural template for the risk-aware layer of a free-flying space manipulator: it shares our regime (fully-actuated 6-DOF base, grappled payload that parametrically changes the dynamics) and addresses precisely the gap between nominal planning and uncertainty handling. The explicit, tunable trade-off between goal-achieving motion and information gain — and the observation that some parameters (I_zz) need deliberate excitation while others (mass) are incidentally excited — is a useful, observability-grounded precedent for designing excitation in our own planner. The Fisher-information / A-optimality cost and the EKF-in-the-loop model update are concrete tools we can compare against chance-constrained or CVaR formulations. The hierarchical global/local/MPC decomposition (motivated by the PSPACE-hardness of informative long-horizon planning) is also relevant to keeping our planner tractable.

Connections

Topics: active_parameter_learning · fisher_information_matrix · inertial_parameter_identification · model_predictive_control · free_flying_vs_free_floating

Key Equations / Quotes

“RATTLE proposes a user-adjustable weighting toward gaining information about parametric uncertainties to aid an online parameter estimator, with the ultimate goal of incorporating model updates.” (Sec. I)

“A cost function is constructed to minimize the trace of the inverse of the FIM, also known as the A-optimality criterion. This is equivalent to minimizing the axis lengths of the uncertainty ellipsoid over the parameters.” (Sec. III-C)

FIM and local objective:

F = Σ_{k=0}^N H(t_k)ᵀ Σ⁻¹ H(t_k) (Eq. 9)

minimize J = Σ_{k=0}^{N−1} x_{t+k}ᵀ Q x_{t+k} + u_{t+k}ᵀ R u_{t+k} + γ tr(F⁻¹) (Eq. 11)

“I_zz in particular saw a large reduction in variance when information-aware planning was used, as rotational excitation was not as frequently used in nominal planning … mass saw little variation … since nominal plans already include translational excitation.” (Sec. IV-B)

Open Questions

• Demonstrations are restricted to 3-DOF granite-table dynamics; the authors flag full 6-DOF ISS cargo transport as future work — does the A-optimality / γ scheme scale to the coupled 6-DOF inertia tensor and CM offset?
• CM offset (c_x, c_y) was not reliably observable in either case; what excitation or estimator changes would render it observable?
• The paper defers robustness/safety guarantees (“future work aims to expand robustness guarantees”); how to compose information-aware excitation with chance constraints or a CVaR risk layer is unresolved.
• How to systematically schedule γ (here a fixed exponential decay) versus the evolving estimator covariance is left open (“discuss RATTLE tuning in further detail”).