# Reinforcement Learning on Cost-Constrained Quadrupedal Hardware

arXiv: https://arxiv.org/abs/2607.26434 · HTML: https://mlsanity.com/paper/2607.26434/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 11 of 11)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [Reinforcement Learning with Random Delays](https://mlsanity.com/paper/2010.02966/) (2020)
- [DiAReL: Reinforcement Learning with Disturbance Awareness for Robust Sim2Real Policy Transfer in Robot Control](https://mlsanity.com/paper/2306.09010/) (2023)
- [Attractor-based models for sequences and pattern generation in neural circuits](https://mlsanity.com/paper/2410.11012/) (2024)
- [Ground contact and reaction force sensing for linear policy control of quadruped robot](https://mlsanity.com/paper/2503.01102/) (2025)

## Abstract (arXiv)

Deploying learned control policies on low-cost robotic platforms introduces transport latencies and noisy motor feedback that systematically widens the sim-to-real gap. The chasm of simulation to deployment in hardware lies in the delay of the actuator reaching the commanded position. On platforms such as the Mini Pupper 2, a measured >50 ms transport delay transforms the locomotion task from a standard Markov decision process into a partially observable one. In this paper, we take a biologically inspired approach of handling noisy and delayed feedback to close the sim-to-real gap, thereby expanding the capability of reinforcement learning on cost-constrained hardware. Using a low-cost quadrupedal hardware platform, we find that using a forward model of the average actuator delay, paired with a time-aware neural network results in robust locomotion. Additionally, our time-aware neural network learned a central pattern generator (CPG): a self-sustaining rhythmic gait that is robust to +320 ms latency perturbations, mirroring the CPGs found in the spinal cords of vertebrates. We posit that temporal self-organization may be a general strategy for cost-constrained locomotion.