An open research question in robotics is how to combine the benefits of model-free reinforcement learning (RL)—known for its strong task performance and flexibility in optimizing general reward formulations—with the robustness and online replanning capabilities of model predictive control (MPC). This paper provides an answer by introducing a new framework called Actor-Critic Model Predictive Control. The key idea is to embed a differentiable MPC within an actor-critic RL framework. The proposed approach leverages the short-term predictive optimization capabilities of MPC with the exploratory and end-to-end training properties of RL. The resulting policy effectively manages both short-term decisions through the MPC-based actor and long-term prediction via the critic network, unifying the benefits of both model-based control and end-to-end learning. We validate our method in both simulation and the real world with a quadcopter platform across various high-level tasks. We show that the proposed architecture can achieve real-time control performance, learn complex behaviors via trial and error, and retain the predictive properties of the MPC to better handle out of distribution behaviour.

Robot multimodal locomotion encompasses the ability to transition between walking and flying, representing a significant challenge in robotics. This work presents an approach that enables automatic smooth transitions between legged and aerial locomotion. Leveraging the concept of Adversarial Motion Priors, our method allows the robot to imitate motion datasets and accomplish the desired task without the need for complex reward functions. The robot learns walking patterns from human-like gaits and aerial locomotion patterns from motions obtained using trajectory optimization. Through this process, the robot adapts the locomotion scheme based on environmental feedback using reinforcement learning, with the spontaneous emergence of mode-switching behavior. The results highlight the potential for achieving multimodal locomotion in aerial humanoid robotics through automatic control of walking and flying modes, paving the way for applications in diverse domains such as search and rescue, surveillance, and exploration missions. This research contributes to advancing the capabilities of aerial humanoid robots in terms of versatile locomotion in various environments. Video: https://youtu.be/mi6Do-x67CM

Over the last decade, the use of autonomous drone systems for surveying, search and rescue, or last-mile delivery has increased exponentially. With the rise of these applications comes the need for highly robust, safety-critical algorithms that can operate drones in complex and uncertain environments. Additionally, flying fast enables drones to cover more ground, increasing productivity and further strengthening their use case. One proxy for developing algorithms used in high-speed navigation is the task of autonomous drone racing, where researchers program drones to fly through a sequence of gates and avoid obstacles as quickly as possible using onboard sensors and limited computational power. Speeds and accelerations exceed over 80 kph and 4 g, respectively, raising significant challenges across perception, planning, control, and state estimation. To achieve maximum performance, systems require real-time algorithms that are robust to motion blur, high dynamic range, model uncertainties, aerodynamic disturbances, and often unpredictable opponents. This survey covers the progression of autonomous drone racing across model-based and learning-based approaches. We provide an overview of the field, its evolution over the years, and conclude with the biggest challenges and open questions to be faced in the future.

Recently, Model Predictive Contouring Control (MPCC) has arisen as the state-of-the-art approach for model-based agile flight. MPCC benefits from great flexibility in trading-off between progress maximization and path following at runtime without relying on globally optimized trajectories. However, finding the optimal set of tuning parameters for MPCC is challenging because (i) the full quadrotor dynamics are non-linear, (ii) the cost function is highly non-convex, and (iii) of the high dimensionality of the hyperparameter space. This paper leverages a probabilistic Policy Search method—Weighted Maximum Likelihood (WML)—to automatically learn the optimal objective for MPCC. WML is sample-efficient due to its closed-form solution for updating the learning parameters. Additionally, the data efficiency provided by the use of a model-based approach allows us to directly train in a high-fidelity simulator, which in turn makes our approach able to transfer zero-shot to the real world. We validate our approach in the real world, where we show that our method outperforms both the previous manually tuned controller and the state-of-the-art auto-tuning baseline reaching speeds of 75 km/h.

In this article, we tackle the problem of flying time-optimal trajectories through multiple waypoints with quadrotors. State-of-the-art solutions split the problem into a planning task—where a global time-optimal trajectory is generated—and a control task—where this trajectory is accurately tracked. However, at the current state, generating a time-optimal trajectory that considers the full quadrotor model requires solving a difficult time allocation problem via optimization, which is computationally demanding (in the order of minutes or even hours). This is detrimental for replanning in the presence of disturbances. We overcome this issue by solving the time allocation problem and the control problem concurrently via Model Predictive Contouring Control (MPCC). Our MPCC optimally selects the future states of the platform at runtime, while maximizing the progress along the reference path and minimizing the distance to it. We show that, even when tracking simplified trajectories, the proposed MPCC results in a path that approaches the true time-optimal one, and which can be generated in real time. We validate our approach in the real world, where we show that our method outperforms both the current state of the art and a world-class human pilot in terms of lap time achieving speeds of up to 60 km/h.

Accurate trajectory-tracking control for quadrotors is essential for safe navigation in cluttered environments. However, this is challenging in agile flights due to nonlinear dynamics, complex aerodynamic effects, and actuation constraints. In this article, we empirically compare two state-of-the-art control frameworks: the nonlinear-model-predictive controller (NMPC) and the differential-flatness-based controller (DFBC), by tracking a wide variety of agile trajectories at speeds up to 20 m/s (i.e., 72 km/h). The comparisons are performed in both simulation and real-world environments to systematically evaluate both methods from the aspect of tracking accuracy, robustness, and computational efficiency. We show the superiority of the NMPC in tracking dynamically infeasible trajectories, at the cost of higher computation time and risk of numerical convergence issues. For both methods, we also quantitatively study the effect of adding an inner loop controller using the incremental nonlinear dynamic inversion method, and the effect of adding an aerodynamic drag model. Our real-world experiments, performed in one of the world’s largest motion capture systems, demonstrate more than 78% tracking error reduction of both NMPC and DFBC, indicating the necessity of using an inner loop controller and aerodynamic drag model for agile trajectory tracking.