A Q-learning approach to the continuous control problem of robot inverted pendulum balancing

A Q-learning Approach to the Continuous Control Problem of Robot Inverted Pendulum Balancing

The paper "A Q-learning approach to the continuous control problem of robot inverted pendulum balancing" by Mohammad Safeea and Pedro Neto offers an evaluation of applying discrete-action reinforcement learning (specifically Q-learning) to a challenging continuous control problem: the balancing of an inverted pendulum using a robotic manipulator.

Introduction

The authors introduce the application of reinforcement learning (RL) in robotics, emphasizing its potential to enable autonomous learning in unstructured environments. The study addresses the complexities involved in using RL for continuous control tasks, particularly the inverted pendulum problem. The paper places this work in context by citing key studies and methodologies in RL, highlighting the unique challenges of environment exploration with sparse rewards and the use of simulated environments to train RL policies.

Methodologies

The authors propose a methodology that relies on training the Q-learning policy in a simulated environment before transferring the learned policy to a real robotic system. The simulation is conducted using the Virtual Robot Experimentation Platform (V-REP, CoppeliaSim), and the learned policy is then applied to a real robotic manipulator tasked with balancing an inverted pendulum.

Mathematical Model and System Identification

The system's dynamics are initially modeled mathematically using data acquired from the real-world system. A curve fitting approach is used to derive accurate parameter estimates, ensuring the simulation closely mirrors the actual physical system. This step is crucial for reducing discrepancies between the simulated and real environments, thereby increasing the likelihood of successful policy transfer.

Acceleration Control

The commanded accelerations required to perform the balancing act are tracked using a Closed Loop Inverse Kinematics (CLIK) algorithm. This algorithm, anchored in differential kinematics, ensures that the robot's joints move in a manner that tracks the desired accelerations of the end-effector, which ultimately controls the pendulum.

Implementation

Discretization

Critical to this approach is the discretization of state spaces and action spaces. The authors discretize the control commands, pendulum angular positions and velocities, as well as the robot flange's position and velocity into specific intervals, thus converting a continuous control problem into a discrete one suitable for Q-learning.

Simulation

The Q-learning algorithm undergoes extensive training in the simulated environment. The training process involves 10,000 episodes, with noise injected into the system's parameters to account for uncertainties and enhance robustness.

Results

Upon completing the simulated training, the learned policy is deployed to the real robotic system. The results show that the robot successfully balances the pendulum for approximately five seconds before failure due to cumulative errors and perturbations in the real system.

Discussion and Implications

The study demonstrates the feasibility of using a discrete action RL approach for continuous control tasks when supported by accurate simulations. The advantages of this methodology include significant reductions in training time and risks associated with hardware damage, as well as the control flexibility afforded by starting simulations from various initial states.

However, the authors acknowledge the challenges associated with discrepancies between simulated models and real-world conditions. Even with a robust simulation, unmodeled dynamics and perturbations can undermine performance. Thus, future work is geared towards refining the control policy with more real-world data to further bridge the sim-to-real gap.

Conclusion

This research underscores the potential of combining Q-learning with a carefully modeled simulation environment to address continuous control problems in robotics. Although there are inherent difficulties in directly transferring learned policies from simulation to real-world conditions, this study presents a promising approach that leverages the strengths of RL while proposing future improvements to mitigate its current limitations.

Overall, this paper provides a methodologically sound and practically relevant exploration of the applicability of Q-learning to continuous control problems, contributing valuable insights to the field of robotic control and RL.