Nuclear fusion using magnetic confinement, in particular in the tokamak configuration, is a promising path towards sustainable energy. A core challenge is to shape and maintain a high-temperature plasma within the tokamak vessel. This requires high-dimensional, high-frequency, closed-loop control using magnetic actuator coils, further complicated by the diverse requirements across a wide range of plasma configurations. In this work, we introduce a previously undescribed architecture for tokamak magnetic controller design that autonomously learns to command the full set of control coils. This architecture meets control objectives specified at a high level, at the same time satisfying physical and operational constraints. This approach has unprecedented flexibility and generality in problem specification and yields a notable reduction in design effort to produce new plasma configurations. We successfully produce and control a diverse set of plasma configurations on the Tokamak à Configuration Variable1,2, including elongated, conventional shapes, as well as advanced configurations, such as negative triangularity and ‘snowflake’ configurations. Our approach achieves accurate tracking of the location, current and shape for these configurations. We also demonstrate sustained ‘droplets’ on TCV, in which two separate plasmas are maintained simultaneously within the vessel. This represents a notable advance for tokamak feedback control, showing the potential of reinforcement learning to accelerate research in the fusion domain, and is one of the most challenging real-world systems to which reinforcement learning has been applied.

In this work we present a whole-body Nonlinear Model Predictive Control approach for Rigid Body Systems subject to contacts. We use a full dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences and timings are not prespecified but optimized by the solver. Yet, thorough numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state of the art by at least one order of magnitude. Hardware experiments in form of periodic and non-periodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability and robustness of the approach.

This paper presents a framework for real-time, full-state feedback, unconstrained, nonlinear model predictive control that combines trajectory optimization and tracking control in a single, unified approach. The proposed method uses an iterative optimal control algorithm, namely Sequential Linear Quadratic (SLQ), in a Model Predictive Control (MPC) setting to solve the underlying nonlinear control problem and simultaneously derive the optimal feedforward and feedback terms. Our customized solver can generate trajectories of multiple seconds within only a few milliseconds. The performance of the approach is validated on two different hardware platforms, an AscTec Firefly hexacopter and the ball balancing robot Rezero. In contrast to similar approaches, we perform experiments that require leveraging the full system dynamics.

Abstract-In this paper, we present an efficient Dynamic Programing framework for optimal planning and control of legged robots. First we formulate this problem as an optimal control problem for switched systems. Then we propose a multi-level optimization approach to find the optimal switching times and the optimal continuous control inputs. Through this scheme, the decomposed optimization can potentially be done more efficiently than the combined approach. Finally, we present a continuous-time constrained LQR algorithm which simultaneously optimizes the feedforward and feedback controller with O(n) time-complexity. In order to validate our approach, we show the performance of our framework on a quadrupedal robot. We choose the Center of Mass dynamics and the full kinematic formulation as the switched system model where the switching times as well as the contact forces and the joint velocities are optimized for different locomotion tasks such as gap crossing, walking and trotting.