Autonomous mobile robots have become increasingly capable over the past decades, enabling their use in domains such as logistics, agriculture, and healthcare. This thesis contributes to a collaborative project between the Dutch National Police and the Delft University of Technology, focusing on search and rescue operations in the security domain.

In these safety-critical missions, robots are expected to support human first responders by exploring unknown and potentially hazardous environments, including buildings and natural terrains. To reduce the cognitive and operational burden on human operators, robots must navigate cluttered spaces both autonomously and safely. In the context of this thesis, autonomy refers to onboard decision-making and safety to avoiding collisions despite uncertainties like sensor noise or environmental effects.

This thesis explores autonomous and safe navigation using model predictive control (MPC), a planning and control strategy that predicts future behavior based on a system model and optimizes actions accordingly. MPC’s strength lies in its ability to handle constraints such as actuator limits and obstacle avoidance. However, applying MPC in real-world navigation presents several challenges, which this thesis addresses through the following contributions.

Navigating a mobile robot through cluttered environments requires it to follow dynamic trajectories while avoiding obstacles. Although MPC is well-suited for this task, recent methods for collision-free trajectory tracking often rely on complex mathematical formulations that can be difficult to interpret and apply. Chapter 2 aims to bridge this gap by offering a structured, step-by-step guide. It explains how to model the robot’s navigation problem, formulate the corresponding MPC problem, and establish performance and safety guarantees.

The chapter presents three formulations: a nominal MPC approach for ideal conditions, a robust MPC formulation that accounts for bounded disturbances, and a robust output-feedback MPC formulation that additionally handles measurement noise. Each formulation is supported by theoretical insights and practical considerations. While not exhaustive, the guide is intended to support researchers and practitioners in implementing MPC-based navigation under varying levels of uncertainty.

To enable autonomy, the MPC formulations introduced in Chapter 2 must operate in real time. This is challenging because MPC relies on solving an optimization problem at each time step, which can be computationally demanding. Planning long-term trajectories and computing control commands at high frequency on embedded hardware is especially difficult.

Chapter 3 addresses this by introducing a hierarchical MPC (HMPC) framework that separates planning and control into two layers. The planning MPC handles long-term trajectory generation at a lower frequency, while the tracking MPC focuses on short-term execution at a higher frequency. This separation allows the use of complex nonlinear models in both layers without compromising real-time performance. The tracking MPC layer, freed from long-term planning, can focus on precise tracking, improving stability and responsiveness.

The HMPC framework also includes a method for generating consistent collision avoidance constraints. Its effectiveness is demonstrated through simulations and lab experiments, showing safer and approximately four times faster goal-reaching compared to a single-layer MPC approach.

While the HMPC framework improves autonomy, it leverages a nominal MPC formulation that assumes perfect models and accurate state data. In practice, mobile robots operate in the presence of model uncertainties and noisy measurements, which can lead to constraint violations such as collisions.

Chapter 4 extends the HMPC framework to address these issues by incorporating robust output-feedback MPC into the tracking layer. This extension, called robust output-feedback hierarchical MPC (ROHMPC), provides formal safety guarantees even in the presence of disturbances and measurement noise. Synthesizing the ROHMPC scheme requires knowledge of uncertainty bounds, which are typically unknown.

To overcome this, the chapter introduces an efficient and modular pipeline that estimates these bounds from experimental data, performs necessary offline computations, calibrates constraint tightening to reduce conservatism, and implements the complete control scheme. The pipeline is released as an open-source software package to support reproducibility and future research. Using this pipeline, the chapter demonstrates the successful validation of the ROHMPC framework properties on a simulated quadcopter platform in Gazebo, with reproducible results.

The HMPC and ROHMPC frameworks address autonomy and safety respectively, but successful deployment in real-world scenarios also depends on the reliability of the system. A key aspect of reliability is reproducibility: the ability to consistently generate similar results.

Chapter 5 explores this concept in the context of robotics, defining reproducibility and analyzing how it applies to the hardware-software setups used in earlier chapters. The HMPC framework satisfies method reproducibility, meaning its implementation can be consistently reproduced. However, due to asynchronous processes and non-deterministic code components, it does not fully achieve results reproducibility.

In contrast, the ROHMPC framework satisfies both method and results reproducibility, reinforcing the credibility of the framework. By raising awareness of reproducibility challenges and offering practical insights, this chapter aims to support the development of more robust and trustworthy robotic systems.

All results presented in this thesis have been made publicly accessible through submissions to peer-reviewed venues, an open-access preprint server, and the release of open-source software packages. These results highlight the effectiveness of hierarchical MPC in both simulation and laboratory settings, and demonstrate how formal safety guarantees can be achieved under uncertainty.

To support future research, Chapter 6 summarizes the key contributions and outlines several promising directions for further exploration. These include extending the proposed algorithms to 3D environments, integrating onboard sensing for autonomous outdoor navigation, and incorporating data-driven methods to reduce conservatism.

To efficiently deploy robotic systems in society, mobile robots must move autonomously and safely through complex environments. Nonlinear model predictive control (MPC) methods provide a natural way to find a dynamically feasible trajectory through the environment without colliding with nearby obstacles. However, the limited computation power available on typical embedded robotic systems, such as quadrotors, poses a challenge to running MPC in real time, including its most expensive tasks: constraints generation and optimization. To address this problem, we propose a novel hierarchical MPC scheme that consists of a planning and a tracking layer. The planner constructs a trajectory with a long prediction horizon at a slow rate, while the tracker ensures trajectory tracking at a relatively fast rate. We prove that the proposed framework avoids collisions and is recursively feasible. Furthermore, we demonstrate its effectiveness in simulations and lab experiments with a quadrotor that needs to reach a goal position in a complex static environment. The code is efficiently implemented on the quadrotor's embedded computer to ensure real-time feasibility. Compared to a state-of-the-art single-layer MPC formulation, this allows us to increase the planning horizon by a factor of 5, which results in significantly better performance.

The free energy principle from neuroscience provides a brain-inspired perception scheme through a data-driven model learning algorithm called Dynamic Expectation Maximization (DEM). This paper aims at introducing an exper-imental design to provide the first experimental confirmation of the usefulness of DEM as a state and input estimator for real robots. Through a series of quadcopter flight experiments under unmodelled wind dynamics, we prove that DEM can leverage the information from colored noise for accurate state and input estimation through the use of generalized coordinates. We demonstrate the superior performance of DEM for state es-timation under colored noise with respect to other benchmarks like State Augmentation, SMIKF and Kalman Filtering through its minimal estimation error. We demonstrate the similarities in the performance of DEM and Unknown Input Observer (UIO) for input estimation. The paper concludes by showing the influence of prior beliefs in shaping the accuracy-complexity trade-off during DEM's estimation.

This paper presents a rule-compliant trajectory optimization method for the guidance and control of autonomous surface vessels. The method builds on Model Predictive Contouring Control and incorporates the International Regulations for Preventing Collisions at Sea - known as COLREGs - relevant for motion planning. We use these traffic rules to derive a trajectory optimization algorithm that guarantees safe navigation in mixed-traffic conditions, that is, in traffic environments with human operated vessels. The choice of an optimization-based approach enables the formalization of abstract verbal expressions, such as traffic rules, and their incorporation in the trajectory optimization algorithm along with the dynamics and other constraints that dictate the system's evolution over a sufficiently long receding horizon. The ability to plan considering different types of constraints over a long horizon in a unified manner leads to a proactive motion planner that mimics rule-compliant maneuvering behavior. The efficacy of the derived algorithm is validated in different simulation scenarios.