Learning On The Job: Zero-Shot Task Execution under Parametric Uncertainty via Trajectory-Parametrized Dual Control

Victor Vantilborgh; Hrishikesh Sathyanarayan; Guillaume Crevecoeur; Ian Abraham; Tom Lefebvre

cs.ROOct 23, 2025

Learning On The Job: Zero-Shot Task Execution under Parametric Uncertainty via Trajectory-Parametrized Dual Control

Authors: Victor Vantilborgh, Hrishikesh Sathyanarayan, Guillaume Crevecoeur, Ian Abraham, Tom Lefebvre

Organizations: Department of Electromechanical, Systems and Metal Engineering, Ghent University, Belgium · Department of Mechanical Engineering, Yale University, USA

Abstract

Model-based control can achieve reliable task performance, but its effectiveness depends on the accuracy of the underlying model. Robots operating under model uncertainty must often adapt to previously unseen payloads, objects, and interaction dynamics to complete a task successfully. Conventional approaches typically rely on a dedicated task- and control-agnostic excitation phase for estimating physics parameters, delaying task execution and collecting potentially irrelevant data. In this paper, we instead consider zero-shot task execution under parametric uncertainty, where online model learning and control proceed concurrently during task execution. Our approach formulates reference generation within a dual control framework to produce task-relevant, informative trajectories that reduce parameter uncertainty in directions critical to task success. We predefine a feedback policy with an explicit parameter adaptation law and optimize the reference through the resulting adaptive closed-loop dynamics. We propose two formulations: 1) minimizing expected task cost under parameter uncertainty, and 2) minimizing optimality loss, which quantifies the degradation in task performance caused by planning with an incorrect parameter estimate. By actively optimizing for informative trajectories via a natural Fisher information measure, we tightly approach a lower bound on task-relevant parameter uncertainty while simultaneously achieving reliable task execution. Across diverse tasks, controllers, and adaptation laws, targeted exploration enables the identification required for successful task execution, allowing robots to learn relevant physical parameters while completing the task in a single attempt.

Figures & tables

Fig. 1 : Comparison of dual control and conventional trajectory planning. The Franka FR3 transports an object with unknown mass distribution and balances it on a narrow tower. Top: our dual control optimized trajectory $d^{\star}$ ; middle: a conventional task-only reference, with the corresponding end-effector paths overlaid. Bottom: schematic evolution of the parameter covariance $\Sigma(t)$ . Under $d^{\star}$ , the task-executing motion also provides task-relevant excitation, reducing uncertainty primarily along parameters that affect task performance, such as the center of mass (CoM), while providing little excitation for parameters such as the moment of inertia that have limited influence on the task. The conventional reference leaves the task-relevant uncertainty largely unresolved.

Fig. 2 : Schematic overview. The reference is optimized offline over samples from the prior, propagated through the closed loop of plant, controller and adaptation law. It is then executed for zero-shot task performance on the real system under the same adaptation control law.

Fig. 3 : Cartpole results. Left: pole-tip paths of the three references. Right, top: relative terminal identification error $\|\hat{\theta}_{T}-\theta^{\star}\|/\|\theta^{\star}\|$ against the true pole mass. Right, bottom: closed-loop sensitivity to the parameter mismatch, measured as the RMS deviation of the executed trajectory from its own reference. Each curve spans the masses at which that reference completes the swing-up and ends in a $\times$ at the first mass at which the pole falls.

	success	tracking	parameter	input	$t_{\rm up}$
	[%]	RMSE [–]	error [–]	cost	[s]
Conv.	$60$	$0.045\pm 0.047$	$0.356\pm 0.140$	$101$	$2.38$
RO	$87$	$0.018\pm 0.006$	$0.329\pm 0.140$	$72$	$2.50$
OL	$93$	$0.036\pm 0.007$	$0.058\pm 0.020$	$119$	$2.40$

TABLE I : Cartpole summary over the mass sweep. Success is the fraction of the

15

true masses at which the swing-up completes; the remaining columns are means

\pm

standard deviations over the

9

masses at which all three references succeed, so the comparison is one-to-one.

Fig. 4 : Cartpole references at the planner prior: cart position and velocity, pole angle and rate, and input force. All three perform a two-swing pump; only OL keeps exciting the system once the pole is upright.

Fig. 5 : Slung-payload references. Left: renders at the planner prior, vehicle path colored and load path gray. Right: realized load paths over the $30$ payload draws in top ( $y$ – $x$ ) and side ( $z$ – $x$ ) view; dashed: reference, $\times$ : failed delivery.

Method	$\|\hat{L}-L^{\star}\|$ [m]	$\\|\Delta p_{L}\\|$ [m]	swing [ ∘ ]	collisions
Conventional	$0.171{\pm}0.086$	$0.205{\pm}0.090$	$10.1{\pm}1.9$	$6/30$
RO	$0.062{\pm}0.017$	$0.084{\pm}0.018$	$6.1{\pm}1.6$	$0/30$
OL	$0.072{\pm}0.024$	$0.093{\pm}0.023$	$5.6{\pm}1.4$	$0/30$

TABLE II : Slung-payload delivery, mean,

\pm

,std over

30

payload draws. Placement error

|p_{L}(T)-p_{\mathrm{pad}}|

at release; swing is the residual amplitude at the drop point. A collision is counted if the payload or vehicle contacts a wall or violates the tunnel floor or ceiling.

Panel of Figure 8 — Fig. 6 : Cable-suspended payload delivery over $30$ payload draws. ( 6(a) ) Relative cable-length error; thin lines are individual draws, thick lines the ensemble mean. ( 6(b) ) Terminal placement error of the payload. ( 6(c) ) Payload trajectory in the $y$ – $z$ plane.

Panel of Figure 9 — Fig. 7 : Designed reference trajectories at the planner prior, and the outcomes they produce over $30$ rods drawn from that prior.

Panel of Figure 10 — Fig. 8 : (a) Relative terminal error grouped by parameter class. (b) Median absolute error of the mass and CoM estimates over the $30$ rods.

	balanced	$\|\Delta m\|/m$	$\|\Delta c\|$	placement
	[-]	[–]	[mm]	error [mm]
Conventional	$5/30$	$0.033\pm 0.013$	$23.5\pm 5.7$	$15.2\pm 0.9$
RO	$27/30$	$0.017\pm 0.012$	$10.7\pm 4.9$	$10.9\pm 3.7$
OL	$30/30$	$0.021\pm 0.012$	$6.7\pm 3.6$	$8.1\pm 3.1$

TABLE III : Rod balancing in simulation,

30

rods drawn from the prior. Mean

\pm

standard deviation.

Panel of Figure 12 — Fig. 9 : Hardware setup. The Franka FR3 grasps one of four test objects — a wooden rod at its center, the same rod $7$ cm off center, a T-shaped assembly, and a hammer — transports it across the workspace and releases it onto the tower. None of the objects was used when designing the references.

	rod	rod	T-shape	hammer	Overall
	(centered)	( $7$ cm off)
Conventional	4/5	0/5	0/5	0/5	4/20
RO	5/5	4/5	3/5	3/5	15/20
OL	5/5	5/5	4/5	3/5	17/20

TABLE IV : Rod balancing on hardware: successful placements out of

5

repetitions per object.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

	Cartpole	Quadrotor with slung load	Franka FR3
Parameters $\theta$	$[m,h,J]$	$[m_{L},L]$	$[m,c,I]\in\mathbb{R}^{10}$
Prior	$m\sim\mathcal{N}(0.30,0.40^{2})$ kg; $h,J$ follow $m$	$m_{L}\sim\mathcal{N}(1.00,0.15^{2})$ kg, $L\sim\mathcal{N}(0.70,0.20^{2})$ m	beam $m_{b}\sim\mathcal{N}(0.65,0.10^{2})$ kg, lump $m_{p}\sim\mathcal{N}(0.45,0.17^{2})$ kg at $d\sim\mathcal{U}(\pm 0.135)$ m
Horizon	$10$ s	$24$ s	$5$ s + $1$ s guarded descent
Reference	direct collocation, $501$ nodes	degree-5 B-spline on load path, $16$ control points	degree-5 joint-space B-spline, $12$ control points/joint
Policy $\pi$	TVLQR, $Q=\mathrm{diag}(1,5,0.1,1)$ , $R=1$	geometric SE(3) [ 40 ] , $k_{x}=6$ , $k_{v}=4$ , $k_{R}=18$ , $k_{\Omega}=3$	Slotine–Li, $\Lambda=8I$ s -1 , $K=\mathrm{diag}(\hat{M})\Lambda$
Adaptation $\rho$	RLS, $\lambda=1$	RLS, $\lambda=1$	composite natural gradient [ 23 ] , $\gamma=1$ , $\kappa=0.3$

Appendix

TABLE V : Implementation settings for the three experimental platforms.

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Planning safe trajectories under model uncertainty is a fundamental challenge. Robust planning ensures safety by considering worst-case realizations, yet ignores uncertainty reduction and leads to overly conservative behavior. Actively reducing uncertainty on-the-fly during a nominal mission defines the dual control problem. Most approaches address this by adding a weighted exploration term to the cost, tuned to trade off the nominal objective and uncertainty reduction, but without formal consideration of when exploration is beneficial. Moreover, safety is enforced in some methods but not in others. We study a budget-constrained dual control problem, where uncertainty is reduced subject to safety and a mission-level cost budget that limits the allowable degradation in task performance due to exploration. In this work, we propose Dual-gatekeeper, a framework that integrates robust planning with active exploration under formal guarantees of safety and budget feasibility. The key idea is that exploration is pursued only when it provides a verifiable improvement without compromising safety or violating the budget, enabling the system to balance immediate task performance with long-term uncertainty reduction in a principled manner. We provide two implementations of the framework based on different safety mechanisms and demonstrate its performance on quadrotor navigation and autonomous car racing case studies under parametric uncertainty.

Abstract

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