Safe-Ballbot: Tilt-Consistent MPC with Control Barrier Functions for Ballbot Navigation

Autonomous mobile robots operating in tight environments require motion planning frameworks that account for the physical footprint of the robot. Simplifying the geometry to a point or a circle is conservative and discards information needed to successfully and safely traverse narrow passages. This work proposes a safe local motion planning and control method that guarantees that a polytopic robot footprint stays inside a continuously updated convex free-space region. The containment condition is formulated as a set of discrete-time control barrier function constraints within a model predictive controller. The number of safety constraints depends on the complexity of the local free-space geometry and the robot shape, instead of the number of obstacles. The proposed free-space formulation does not need any obstacle detection or segmentation. A comparative analysis against a polytope-based obstacle avoidance formulation confirms favorable scaling up to a reduction of 91$\times$ in computation time as the number of obstacles increases. The approach is validated in simulation with an autonomous surface vehicle and on hardware with a non-holonomic mobile robot, using both occupancy grids and LiDAR sensing. The experiments demonstrate safe real-time motion planning and control at 10~Hz on an onboard embedded computer, including reactive avoidance of dynamic obstacles.

Safe and efficient robot navigation in crowds requires anticipating pedestrian motion despite uncertain and potentially shifting prediction errors. Existing reactive methods can produce oscillatory behavior, while predictive planners often treat forecasts as exact or rely on restrictive error models. Incorporating conservative uncertainty sets as hard constraints can also render model predictive control (MPC) infeasible. We propose CoCoNav, a crowd-navigation framework that combines online conformal calibration with runtime-certified planning. A horizon-specific conformal proportional--integral controller adapts trajectory-error bounds to regulate long-run empirical coverage, enabling the framework to respond to changing prediction errors. A relax-then-verify planner preserves solver feasibility by generating nominal trajectories with soft-constrained MPC and separately certifying them, together with contingency maneuvers, against the calibrated bounds before execution. Simulations and quadruped experiments show that CoCoNav achieves a favorable balance among collision avoidance, task success, and navigation efficiency relative to the evaluated baselines.

Control barrier functions (CBFs) have become one of the most popular tools for encoding and enforcing state constraints in safety-critical robotics. Standard CBF approaches are inherently myopic in nature as they enforce safety only at the current time step. Consequently, the system can be driven toward the boundary of the safe set where no feasible safe control exists at a future timestep. Model predictive control (MPC) based approaches address this by enforcing state constraints over a receding horizon. However, such approaches generally require the model to be known for solving a constrained optimization problem at every step, which is computationally expensive for real-time deployment. We propose BarrierFormer, a barrier-supervised transformer framework that addresses these limitations by encoding rollout-level CBF constraints in learning a model-free safe policy. A causal transformer encodes observation-action history, autoregressively generates a predictive rollout through the dynamics head to replace the model, and provides a residual correction to a nominal controller through the action head to replace the online computation. A barrier critic operating on local observations evaluates CBF constraint violations along this rollout, and a safety teacher computes barrier-consistent actions satisfying these constraints as direct supervision targets for the learned control policy. During inference, the policy maps observation-action history to control actions without any online optimization or model knowledge, enabling real-time model-free predictive safety enforcement. Evaluations across linear and nonlinear, 2D and 3D dynamical systems for safe goal-directed navigation demonstrate that BarrierFormer outperforms existing reinforcement learning (RL)-based, diffusion-based, MPC-based, and transformer-based approaches in safety rate and inference latency.