# Closed-Loop Identification and Tracking Control of a Ballbot

arXiv: https://arxiv.org/abs/2404.14845 · HTML: https://mlsanity.com/paper/2404.14845/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2024.

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning for Ballbot Navigation in Uneven Terrain](https://mlsanity.com/paper/2505.18417/) (2025)

## Abstract (arXiv)

Identifying and controlling an unstable, underactuated robot to enable reference tracking is a challenging control problem. In this paper, a ballbot (robot balancing on a ball) is used as an experimental setup to demonstrate and test proposed strategies to tackle this control problem. A double-loop control system, including a state-feedback gain in the outer-loop and a Proportional-Integral-Derivative (PID) controller in the inner-loop, is presented to balance the system in its unstable equilibrium. Once stability is reached, the plant's response to a designed excitation signal is measured and interpreted to identify the system's dynamics. Hereby, the parameters of a linearized model of the ballbot are identified with prior knowledge about the structure of the nonlinear dynamics of the system. Based on an identified linear time-invariant (LTI) state-space model, a double-loop control strategy is considered to balance the real system and to allow reference tracking. A linear quadratic regulator (LQR) is designed offline and implemented in the inner-loop to ensure balance. In the outer-loop, the estimated dynamics forecast the system's behavior online using a model-predictive-control (MPC) design to find the optimal control input for reference tracking. The experimental results demonstrate the applicability of the proposed strategies.