# Deep Reinforcement Learning-Based Motion Planning and PDE Control for Flexible Manipulators

arXiv: https://arxiv.org/abs/2506.08639 · HTML: https://mlsanity.com/paper/2506.08639/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## 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, 6 of 6)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Deep Reinforcement Learning for Robotic Manipulation with Asynchronous Off-Policy Updates](https://mlsanity.com/paper/1610.00633/) (2016)
- [A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms](https://mlsanity.com/paper/1907.03146/) (2019)
- [On the Role of the Action Space in Robot Manipulation Learning and Sim-to-Real Transfer](https://mlsanity.com/paper/2312.03673/) (2023)
- [Integrating DeepRL with Robust Low-Level Control in Robotic Manipulators for Non-Repetitive Reaching Tasks](https://mlsanity.com/paper/2402.02551/) (2024)

## Built on by (most cited first, 2 of 2)

- [Operator-Theoretic Foundations and Policy Gradient Methods for General MDPs with Unbounded Costs](https://mlsanity.com/paper/2603.17875/) (2026)
- [Deep Reinforcement Learning for Adaptive Gain Tuning in Control of Teleoperation Manipulators with Joint Flexibility and Time-Varying Delays](https://mlsanity.com/paper/2607.21145/) (2026)

## Abstract (arXiv)

This article presents a motion planning and control framework for flexible robotic manipulators, integrating deep reinforcement learning (DRL) with a nonlinear partial differential equation (PDE) controller. Unlike conventional approaches that focus solely on control, we demonstrate that the desired trajectory significantly influences endpoint vibrations. To address this, a DRL motion planner, trained using the soft actor-critic (SAC) algorithm, generates optimized trajectories that inherently minimize vibrations. The PDE nonlinear controller then computes the required torques to track the planned trajectory while ensuring closed-loop stability using Lyapunov analysis. The proposed methodology is validated through both simulations and real-world experiments, demonstrating superior vibration suppression and tracking accuracy compared to traditional methods. The results underscore the potential of combining learning-based motion planning with model-based control for enhancing the precision and stability of flexible robotic manipulators.