Micro Neural Policies for Safe Real-Time Robotic Control

Hongpeng Cao; Riccardo Curcio; Daniele Ottaviano; Marco Caccamo

cs.ROOct 6, 2026

Micro Neural Policies for Safe Real-Time Robotic Control

Authors: Hongpeng Cao, Riccardo Curcio, Daniele Ottaviano, Marco Caccamo

Organizations: School of Engineering and Design, Technical University of Munich, Boltzmannstraße 15, 85748 Garching b. München, Germany · Department of Computer Science, Sapienza University of Rome, Via Salaria 113, 00198 Rome, Italy

Abstract

In this paper, we investigate the synthesis of Micro Neural Policies (MNP) to enable safe and robust real-time robotic control on computationally constrained embedded devices. We demonstrate that integrating Evolution Strategy (ES) and Statistical Model Checking (SMC)-based verification for policy search can drastically reduce neural network size without compromising safety and robustness. We conduct a large-scale training and evaluation of MNP on Cartpole and Quadrotor control tasks, varying control frequencies and network architectures. After validating these policies in simulation, we evaluate their deployability through zero-shot transfer to physical systems. Our experiments show that MNP can successfully achieve safe sim-to-real transfer without sacrificing control performance. We then show that the policies' memory footprint, ranging from 0.5 to 7.5 kB, allows deployment on microcontrollers, where they achieve real-time inference latency with under 25 ns of jitter while leaving the chip idle for over 97% of the time for additional workloads. This makes them a highly practical solution for severely resource-constrained robotic systems.

Figures & tables

System	Variable	Constraint	Variable	Constraint
Cartpole	$x_{t}$	$\|x_{t}\|<0.35~\mathrm{m}$	$\theta_{t}$	$\|\theta_{t}\|<0.8~\mathrm{rad}$
	$\dot{x}_{t}$	$\|\dot{x}_{t}\|<2.0~\mathrm{m/s}$	$\dot{\theta}_{t}$	$\|\dot{\theta}_{t}\|<4.0~\mathrm{rad/s}$
	$a_{t}$	$\|a_{t}\|<10~\mathrm{N}$
Quadrotor	$x_{t},y_{t}$	$\|\cdot\|<4.0~\mathrm{m}$	$\phi_{t},\theta_{t}$	$\|\cdot\|<1.5~\mathrm{rad}$
	$z_{t}$	$\|z_{t}\|<2.5~\mathrm{m}$	$\psi_{t}$	$\|\psi_{t}\|<\pi~\mathrm{rad}$
	$\dot{x}_{t},\dot{y}_{t},\dot{z}_{t}$	$\|\cdot\|<5.0~\mathrm{m/s}$	$p_{t},q_{t},r_{t}$	$\|\cdot\|<2.0~\mathrm{rad/s}$

TABLE I : State and action constraints for the Cartpole and Quadrotor systems.

Panel of Figure 2 — Fig. 1 : Real-world experimental platforms: (a) Quanser Cartpole equipped with a Raspberry Pi 4B. (b) ANT-X quadrotor equipped with a Pixhawk flight controller (STM32F427).

Freq.	Metric	DRL	DRL-Res	ES	ES-Res
50 Hz	Verifiability	0/5	3/5	5/5	5/5
	Return Lower Bound	$7.46$ $\pm$ $4.39$	$251.97$ $\pm$ $223.71$	$461.57$ $\pm$ $11.64$	$457.35$ $\pm$ $5.26$
	Relative Enlarged Region ( $\%$ )	—	$0.00$ $\pm$ $0.00$	$96.71$ $\pm$ $3.63$	$96.62$ $\pm$ $3.39$
100 Hz	Verifiability	1/5	2/5	5/5	5/5
	Return Lower Bound	$85.52$ $\pm$ $167.63$	$188.05$ $\pm$ $207.56$	$442.40$ $\pm$ $7.46$	$430.52$ $\pm$ $8.33$
	Relative Enlarged Region ( $\%$ )	$0.00$ $\pm$ $0.00$	$0.00$ $\pm$ $0.00$	$95.50$ $\pm$ $3.01$	$97.79$ $\pm$ $2.57$

TABLE II : Safety and performance comparison in Cartpole simulation at the 50Hz and 100Hz control frequencies.

Freq.	Metric	DRL	DRL-Res	ES	ES-Res
50 Hz	Verifiability	0/5	0/5	3/5	5/5
	Return Lower Bound	$68.71$ $\pm$ $147.02$	$12.61$ $\pm$ $15.24$	$319.60$ $\pm$ $165.26$	$455.69$ $\pm$ $14.33$
	Relative Enlarged Region ( $\%$ )	—	—	$81.64$ $\pm$ $8.93$	$94.13$ $\pm$ $2.87$
100 Hz	Verifiability	0/5	0/5	4/5	5/5
	Return Lower Bound	$2.91$ $\pm$ $5.23$	$12.60$ $\pm$ $16.91$	$300.68$ $\pm$ $137.79$	$424.09$ $\pm$ $32.30$
	Relative Enlarged Region ( $\%$ )	—	—	$85.80$ $\pm$ $15.76$	$87.46$ $\pm$ $6.08$

TABLE III : Safety and performance comparison in Quadrotor simulation at the 50Hz and 100Hz control frequencies.

Fig. 2 : Learning capability evaluation in Cartpole Simulation.

Fig. 3 : Learning capability evaluation in Quadrotor Simulation.

Fig. 4 : Real-world Cartpole evaluation.

Panel of Figure 8 — Fig. 5 : Quadrotor trajectory tracking in simulation and real-world experiments.

System	Architecture	Latency		Flash		RAM		Energy/inference		Power @50 Hz		Power @100 Hz
System	Architecture	ES	ES-Res	ES	ES-Res	ES	ES-Res	ES	ES-Res	ES	ES-Res	ES	ES-Res
Cartpole	2×2	10.26 $\pm$ 0.00 µs	10.10 $\pm$ 0.00 µs	536 B	712 B	40 B	56 B	0.25 $\pm$ 0.07 µJ	0.29 $\pm$ 0.07 µJ	0.69 mW	0.69 mW	0.71 mW	0.70 mW
	4×4	19.72 $\pm$ 0.00 µs	21.13 $\pm$ 0.00 µs	696 B	852 B	40 B	56 B	0.45 $\pm$ 0.05 µJ	0.40 $\pm$ 0.08 µJ	0.70 mW	0.70 mW	0.72 mW	0.71 mW
	8×8	39.50 $\pm$ 0.02 µs	38.41 $\pm$ 0.00 µs	1,016 B	1,172 B	64 B	80 B	0.50 $\pm$ 0.07 µJ	0.55 $\pm$ 0.08 µJ	0.70 mW	0.70 mW	0.73 mW	0.74 mW
	16×16	81.34 $\pm$ 0.00 µs	82.97 $\pm$ 0.00 µs	2,040 B	2,200 B	128 B	144 B	0.98 $\pm$ 0.08 µJ	0.87 $\pm$ 0.08 µJ	0.72 mW	0.72 mW	0.78 mW	0.77 mW
	32×32	219.27 $\pm$ 0.00 µs	206.64 $\pm$ 0.01 µs	5,624 B	5,780 B	256 B	272 B	2.88 $\pm$ 0.09 µJ	2.83 $\pm$ 0.10 µJ	0.81 mW	0.81 mW	0.95 mW	0.98 mW

TABLE IV : On-device inference latency, memory and energy cost for Cartpole and Quadrotor policies.

Fig. 6 : Training time comparison

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ShardNet: Training Neural Controllers with Hard, Non-Convex Constraints

Long Kiu Chung, Shreyas Kousik

Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA.

Neural Network Verification Safety-Critical Control

Open paper AskPDF arXiv

While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints. Existing work often treats safety as a metric to optimize for, which competes with other performance objectives, if training converges at all. Instead, we introduce ShardNet, a neural network architecture that strictly enforces unions of polyhedral constraints by construction, using a differentiable projection layer parameterized by a classification network. The key insight is to embed safety into the neural network's structure, allowing performance to be optimized independently because formal safety guarantees are always given. In contrast with existing neural architectures that can only enforce simple convex constraints, ShardNet enables the first safe-by-construction synthesis of forward-invariant neural network controllers on closed-loop systems where safety constraints are expressed as nonconvex unions of polyhedras or learned value function level sets. To support this, we also introduce a technique to verify and train such value functions correctly as rectified linear unit (ReLU) networks, which has not previously been possible. On double integrator benchmarks drawn from the literature, ShardNet policies maintain 100% safety on verified sets and achieves significantly lower objective loss compared to existing formal methods. Furthermore, our value function training technique also produces safe sets more than 3 times larger than existing verification approaches.

Abstract

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