Omnidirectional robots can be realized using Mecanum wheels or using a suitable arrangement of conventional steerable wheels. The latter group, known as omnidirectional steerable wheeled mobile robots (SWMRs), are known to have a lower cost with respect to the former, and to be more robust thanks to the presence of conventional wheels. Nevertheless, their modeling and control is complex, due to the presence of singularities in their representation. This paper proposes a framework for trajectory tracking of SWMRs using Nonlinear Model Predictive Control (NMPC) based on a real-time iteration scheme. The NMPC generates feasible motions for the robot, avoiding model singularities of the mobile base, together with bounds on driving and steering velocities on the wheels. Our NMPC works alongside a finite state machine, responsible for singularity avoidance during starting and stopping motion, and a state trajectory generation scheme based on dynamic feedback linearization, which makes our framework capable of tracking any trajectory. Our approach is validated on a Neobotix MPO-700 on various trajectories.

Most available schemes used for humanoid walking rely on the separation into a planning phase, typically offline, and a Model Predictive Controller (MPC). Moreover, in order for the MPC to work in real time, simplifying assumptions are made both on the template model and on the constraints so that the underlying optimization problem is a Quadratic Programming (QP). The planner is unaware of the underlying humanoid dynamics and of any disturbance acting on the robot. We present an online Feasibility-Aware Plan Adaptation (FAPA) module which can locally adapt footsteps (positions, timings and orientation) in such a way that it guarantees feasibility of the subsequent Intrinsically Stable MPC (IS-MPC) stage. We present two versions of the proposed scheme: one with a fixed regions assignment for placing the footstep and another one where the regions are selected automatically through mixed-integer programming. Simulation results show the effectiveness of the FAPA scheme.

We address the problem of humanoid locomotion in 3D environments consisting of planar regions with arbitrary inclination and elevation, such as staircases, ramps, and multi-floor layouts. The proposed framework combines an offline randomized footstep planner with an online control pipeline that includes a model predictive controller for gait generation and a whole-body controller for computing robot torque commands. The planner efficiently explores the environment and returns the highest-quality plan it can find within a user-specified time budget, while the control layer ensures dynamic balance and adequate ground friction. The complete framework was evaluated via dynamic simulation in MuJoCo, placing the JVRC1 humanoid in four scenarios of varying complexity.

We address the problem of humanoid locomotion in a 3D environment composed of planar regions with arbitrary inclination and elevation, which includes staircases, ramps, and multi‑floor layouts. The proposed framework couples an off‑line randomized footstep planner with an on‑line control pipeline comprising a model predictive controller and a whole‑body controller which provides the robot torque commands. The planner efficiently explores the environment without predefined motion primitives and returns the highest-quality plan it can find within a user‑specified time budget, while the control layer ensures dynamic balance and adequate ground friction. The complete pipeline is evaluated in MuJoCo using the JVRC1 humanoid across four scenarios of increasing complexity.