Control of a pendulum system: From simulation to reality

TL;DR

The paper addresses safe and cost-effective control design by developing an approximated pendulum model and validating a Linear Quadratic Regulator (LQR) controller in both simulation and hardware. It derives a linearized state-space representation around the unstable fixed point, identifies inertial, damping, and gravitational parameters experimentally, and configures a modified OpenAI Gym environment to test the LQR under white-noise disturbances. Key findings show that the LQR gains $\mathbf{K}_r=[33.345,\;0.159]$ stabilize the system with a time constant of $\tau\approx0.3717\ \mathrm{s}$, and that hardware responses closely match simulated results, supporting the use of simulations for control design. The work demonstrates substantial potential for cost and safety savings in robotics by validating control algorithms in simulation before hardware deployment, and outlines future directions including reinforcement learning and broader underactuated systems.

Abstract

Control theory deals with the study of controlling dynamical systems. Robots today are growing increasingly complex and moving out of factory floors to real world environment. These robots have to interact with real world environment factors such as disturbances and this requires the robot to have a control system that is robust. Testing control algorithms on robots in real world environment can pose critical safety issues and can be financially expensive. This has resulted in a heavy emphasis on using simulation to test control algorithms before deploying them in real world environments. Designing control algorithms is an iterative process that starts with modelling the target system in simulation, designing a controller, testing the controller in simulation and then changing the controller parameters to design a better controller. This report explores how an approximated system model of a target hardware system can be developed, which can then be used to design a LQR controller for the target system. The controller is then tested under a disturbance, on hardware and in simulation, and the system response is recorded. The system response from hardware and simulation are then compared to validate the use of approximated system models in simulation for designing and testing control algorithms.

Figures (39)

• Figure 1: Pendulum system
• Figure 2: Overdamped pendulum state space plot
• Figure 3: Experiment hardware components
• Figure 4: HEBI Actuator Teardown
• Figure 5: HEBI X-series Performance