Learning from Demonstrations Meets Symbolic Control - A Supervisory Control Architecture for Formal Certification of Learned Motion

Ashok Kumar; Mahathi Anand; Angela P. Schoellig; Abdalla Swikir

cs.ROOct 14, 2026

Learning from Demonstrations Meets Symbolic Control - A Supervisory Control Architecture for Formal Certification of Learned Motion

Authors: Ashok Kumar, Mahathi Anand, Angela P. Schoellig, Abdalla Swikir

Organizations: Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE. · Learning Systems and Robotics Lab, Technical University of Munich, Germany.

Abstract

Dynamical system (DS)-based learning from demonstration generates flexible robot motions, but existing guarantees rely on certificate generation to obtain formal guarantees of safety and goal convergence. We propose a symbolic supervisory control architecture that automatically generates a fail-safe backup plan, certifying safety, reachability, and actuator feasibility directly from the robot's dynamics, independent of the learned DS. A nominal controller tracks the learned DS, while the supervisory controller monitors safety and target convergence, providing non-conservative intervention when the nominal controller violates necessary constraints. Experimental results include simulations and real robot deployment with various 2D and 3D datasets, including handwriting datasets, validating the effectiveness of our approach in providing formal guarantees with learned motion even in complex, dynamic environments.

Figures & tables

Fig. 1: The proposed pipeline follows the principle synthesize, supervise, and certify . Starting with the learned DS and a symbolic certified controller, our methodology synthesizes nominal controllers to follow the learned paths, supervises and checks for collision and reachability to the goal, and modifies the controller slightly to obtain certified inputs before executing them on the robot.

Fig. 2: Simulations showing the performance of our supervisory control method vs CLF-CBF [ 13 ] for four representative datasets: sine, G, snake, and khamesh, with different obstacle configurations.

Fig. 3: Online realization of our approach vs CLF-CBF on dynamic obstacles with sine motion; red arrows indicate the motion of the obstacles.

method	task success	collisions	vel. limit violations	acc. limit violations	path return rate
ours (Certified Supervisor)	95.67	0.0	0.0	0.0	93.33
CLF-CBF	65.67	18.0	0.0	43.33	53.33

TABLE I: Quantitative comparison on the task performance rates between our method and CLF-CBF. All criteria are evaluated over

300

aggregated DS-learning and tracking tasks, and are measured in

\%

Method	MSE(mm)	DTW(mm)	acc. variation (m/s 2 )	navigation time (s)
Ours (Certified Supervisor)	7.46	14.613	0.249	23.27
CLF-CBF	18.98	17.551	0.02	24.5

TABLE II: Trajectory-fidelity and motion-quality comparison between the our method and the CLF-CBF baseline. All values are averaged over successful trials, aggregated across

10

LASA datsets,

3

learned ds models per motion ( lpv -DS, PolyDS, and NN-DS), and

10

motion trajectories per model.

Learning Method	Trials	ours	CBF-CLF
LPV-DS	100	$99.00\%$	$54.00\%$
PolyDS	100	$100.00\%$	$76.00\%$
NNDS	100	$88.00\%$	$67.00\%$

TABLE III: The learning method-family wise breakdown of the task success rates (ours vs CLF-CBF [ 13 ] ).

Fig. 4: Franka FR3 robot executing a learned C-shaped motion under manually applied perturbations, without an obstacle (left) and with a moving obstacle (right)

Fig. 5: End-effector trajectories when subject to perturbations at runtime using offline (left) and online (right) symbolic synthesis.

Robotic Control

Robotic control studies how machines use sensing and computation to produce reliable movement and interaction in changing environments.

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Sep 29, 2026J/K move · Enter open · S save

A Reachability-based Safety Certificate for Dynamical System Motion Policies

Aditya Vats, Tianyi Xia, Nadia Figueroa

The authors are with the University of Pennsylvania, Philadelphia, PA, USA.

Reachability Analysis Safety-Critical Control Control Barrier Functions Safe Motion Planning

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Dynamical Systems (DS) are reactive motion policies representing vector fields trained with theoretical guarantees of stability and convergence. To ensure safety during deployment in unknown environments they must be locally reshaped, either through modulation or geometric control barrier function strategies. However, depending on the geometry of the obstacles and the complexity of the DS, these local strategies can lead the system to unavoidable collisions or spurious attractors. In this work, we certify safety with a value function drawn from the notion of backward reachability tube, which measures the worst-case safety along a rollout trajectory of the nominal DS. Usually, such a value function is intractable for a controlled system due to curse of dimensionality. We show that in the DS-based learning-from-demonstration setting, the absence of a control input collapses the reachability problem to a deterministic rollout, and the presence of certain stability conditions truncates the infinite horizon to a finite one, resulting in a well-defined value function. We further show that the value function we devised is the maximal forward-invariant subset of the obstaclefree region for the nominal DS flow. The application of this certificate function is validated across five DS constructions - analytical, Neural ODE, diffeomorphic latent space, LPV-DS, SE(3)and validate it on a Franka manipulator. Modulation and geometric CBFs also suffer from saddle point in cases of headon approach towards an unsafe zone. We show that CBF-on-V avoids this pitfall entirely.

Abstract

Robotic Control

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