Safe-Ballbot: Tilt-Consistent MPC with CBFs for Ballbot Navigation

TL;DR

A ballbot must lean to accelerate. Our jerk-model MPC-CBF never asks for more lean than the tracker allows, and conformal prediction handles unpredictable obstacles.

Jerk-model MPC-CBF

A simple planning model with control barrier functions for collision avoidance.

Tilt-consistent bound

Acceleration is limited by the steepest lean the tracker can safely reach.

HSMC-ESO-ECBF tracker

Tilt-safe tracking that keeps the lean angle below its limit.

Conformal prediction

Predicted obstacles are inflated to cover unpredictable motion.

Two-layer control architecture: planning layer with prediction, conformal inflation and jerk-model MPC with obstacle CBFs; tracking layer with ESO, HSMC, ECBF and yaw LQR; torque allocation to the ballbot in MuJoCo — Two-layer architecture. The planner replans every Δt; the tracker closes the loop on the measured state every T_s.

MuJoCo simulation

All experiments run on a high-fidelity, contact-rich MuJoCo model of the ballbot rather than on the simplified models used for design. The controllers and the planner never see this model; they only act on it.

The robot model is adapted from the open-source asRoBallet MuJoCo model.

Free-floating body balancing on a ball, driven by three omni wheels spaced 120° apart with axles tilted 45°.
Every passive roller of the omni wheels is simulated, with its own contacts against the ball.
Ball–floor contact with sliding, torsional and rolling friction on an elliptic friction cone.
Coulomb friction and damping in the wheel and roller joints, absent from the design models.
Wheel torques saturated at ±4 N·m; controllers run at the simulation rate.

passive rollers in contact with the ball

2 ms

time step (500 Hz), implicit integrator

6-D

ball–floor friction: sliding, torsional, rolling

±4 N·m

wheel torque limit

The ballbot in MuJoCo: three-quarter view, omni-wheel axes and roller frames, contact points and forces — (a) Balancing robot, (b) omni wheel with its axis and roller frames, (c) roller–ball and ball–floor contact points (blue) and forces (red).

Balance and tilt-safe tracking

Balance control

Tilt-safe tracking

Obstacle avoidance

Predefined obstacles

Suddenly turning obstacle

Path following

Random moving obstacles

BibTeX

@article{safeballbot2026,
  title  = {Safe-Ballbot: Tilt-Consistent {MPC} with Control Barrier Functions for Ballbot Navigation},
  author = {Anonymous},
  year   = {2026},
  note   = {Under review}
}