Marco Gabiccini

This paper presents a simulation-based methodology for automated tuning of a triple-loop controller (steering, throttle, and braking) for a Dallara single-seater race car. The approach targets on-track driving at handling limits, where strong nonlinearities and coupled dynamics dominate, treating the vehicle as a black box. Five controller gains are optimized via derivative-free pattern search, using reference trajectories from a professional driver in a Driver-in-the-Loop (DiL) simulator. Human-likeness is promoted by penalty terms on state and control trajectories while maximizing distance over a fixed horizon as a proxy for lap-time reduction. The application uses a high-fidelity multibody vehicle model with realistic tire, suspension, and actuator dynamics in the DiL environment, rather than simplified single-track representations. Contributions are: (i) effective application of derivative-free optimization to complex, high-dimensional, black-box vehicle systems; and (ii) a systematic, reproducible procedure for automatic tuning of controller parameters with a predetermined architecture to reproduce a professional driver’s performance and embed human-likeness. Optimization required approximately 2.4 h. Results show that the optimized controller improves track coverage by 63.6 m (1.1% increase) compared to manual tuning while maintaining a realistic driving style, offering a more systematic and reliable solution than manual, trial-and-error calibration.

This work estimates safe invariant subsets of the Region of Attraction (ROA) for a seven-state vehicle-with-driver system, capturing both asymptotic stability and the influence of state-safety bounds along the system trajectory. Safe sets are computed by optimizing Lyapunov functions through an original iterative Sum-of-Squares (SOS) procedure. The method is first demonstrated on a two-state benchmark, where it accurately recovers a prescribed safe region as the 1-level set of a polynomial Lyapunov function. We then describe the distinguishing characteristics of the studied vehicle-with-driver system: the control dynamics mimic human driver behavior through a delayed preview-tracking model that, with suitable parameter choices, can also emulate digital controllers. To enable SOS optimization, a polynomial approximation of the nonlinear vehicle model is derived, together with its operating-envelope constraints. The framework is then applied to understeering and oversteering scenarios, and the estimated safe sets are compared with reference boundaries obtained from exhaustive simulations. The results show that SOS techniques can efficiently deliver Lyapunov-defined safe regions, supporting their potential use for real-time safety assessment, for example as a supervisory layer for active vehicle control.

This letter presents a trajectory planner for humanoid robots to perform dynamic motions on complex, parameterizable terrains using a contact-implicit whole-body optimization framework. The planner generates feasible movements without predefined contact sequences, considering the robot full dynamics and kinematics. To plan bipedal locomotion on steps, ramps, and other terrains, we propose a mathematical model to approximate ground geometry with a smooth surface. The rigid interaction between the robot and the ground is modeled via novel contact constraints, extending the domain of applicability from flat and horizontal surfaces to any arbitrary smooth surface. Effectiveness is demonstrated using nonlinear programming to plan motions on various terrain topologies. We also explore dynamic trajectory generation by embedding high-level requirements in the cost function and the initial guess. Preliminary feasibility tests were conducted over non-coplanar terrains, both in simulation and on the real robot ErgoCub.

Robust control techniques are crucial for deploying robotic solutions in real applications and handling model uncertainties in robotic manipulators. The inertial parameters are fundamental to implementing control algorithms. While theoretical approaches to compute the system dynamics and the regressor matrix are well-established, they are computationally expensive and a practical implementation framework is still lacking. To address this challenge, we developed a new and efficient method to compute the Coriolis matrix based on Christoffel’s symbols. The result forms the basis of Thunder Dynamics, an open-source software package able to create standalone libraries that compute the system kinematics and dynamics for real-time adaptive control implementation. Thunder Dynamics enables users to create and compile user-defined functions on a robot, which can then be used in C++ or Python 3. To test the proposed framework, we implemented a Cartesian adaptive backstepping controller with axis-angle orientation using our tool. We tested the controller on a seven-degrees-of-freedom manipulator in both simulation and real-world scenarios, varying the levels of uncertainties in the inertial parameters. The results demonstrated that Thunder Dynamics is capable of meeting computational constraints given by the control loop frequency of real systems, permitting, for example, the implementation of advanced controls on commercial manipulators.

This paper presents a disturbance-aware framework that embeds robustness into minimum-lap-time trajectory optimization for motorsport. Two formulations are introduced. (i) Open-loop, horizon-based covariance propagation uses worst-case uncertainty growth over a finite window to tighten tire-friction and track-limit constraints. (ii) Closed-loop, covariance-aware planning incorporates a time-varying LQR feedback law in the optimizer, providing a feedback-consistent estimate of disturbance attenuation and enabling sharper yet reliable constraint tightening. Both methods yield reference trajectories for human or artificial drivers: in autonomous applications the modelled controller can replicate the on-board implementation, while for human driving accuracy increases with the extent to which the driver can be approximated by the assumed time-varying LQR policy. Computational tests on a representative Barcelona-Catalunya sector show that both schemes meet the prescribed safety probability, yet the closed-loop variant incurs smaller lap-time penalties than the more conservative open-loop solution, while the nominal (non-robust) trajectory remains infeasible under the same uncertainties. By accounting for uncertainty growth and feedback action during planning, the proposed framework delivers trajectories that are both performance-optimal and probabilistically safe, advancing minimum-time optimization toward real-world deployment in high-performance motorsport and autonomous racing.