We present a single Trajectory Optimization formulation for legged locomotion that automatically determines the gait-sequence, step-timings, footholds, swing-leg motions and 6D body motion over non-flat terrain, without any additional modules. Our phase-based parameterization of feet motion and forces allows to optimize over the discrete gait sequence using only continuous decision variables. The system is represented using a simplified Centroidal dynamics model that is influenced by the feet's location and forces. We explicitly enforce friction cone constraints, depending on the shape of the terrain. The NLP solver generates highly dynamic motion-plans with full flight-phases for a variety of legged systems with arbitrary morphologies in an efficient manner. We validate the feasibility of the generated plans in simulation and on the real quadruped robot ANYmal. Additionally, the entire solver software TOWR used to generate these motions is made freely available.

Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of oscillators, from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule. One major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive oscillator. The convergence of the learning is proved for the Hopf oscillator, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic oscillators like relaxation oscillators and strange attractors.

One of the hallmarks of the performance, versatility, and robustness of biological motor control is the ability to adapt the impedance of the overall biomechanical system to different task requirements and stochastic disturbances. A transfer of this principle to robotics is desirable, for instance to enable robots to work robustly and safely in everyday human environments. It is, however, not trivial to derive variable impedance controllers for practical high degree-of-freedom (DOF) robotic tasks. In this contribution, we accomplish such variable impedance control with the reinforcement learning (RL) algorithm PI 2 (Policy Improvement with Path Integrals). PI 2 is a model-free, sampling-based learning method derived from first principles of stochastic optimal control. The PI 2 algorithm requires no tuning of algorithmic parameters besides the exploration noise. The designer can thus fully focus on the cost function design to specify the task. From the viewpoint of robotics, a particular useful property of PI 2 is that it can scale to problems of many DOFs, so that reinforcement learning on real robotic systems becomes feasible. We sketch the PI 2 algorithm and its theoretical properties, and how it is applied to gain scheduling for variable impedance control. We evaluate our approach by presenting results on several simulated and real robots. We consider tasks involving accurate tracking through via points, and manipulation tasks requiring physical contact with the environment. In these tasks, the optimal strategy requires both tuning of a reference trajectory and the impedance of the end-effector. The results show that we can use path integral based reinforcement learning not only for planning but also to derive variable gain feedback controllers in realistic scenarios. Thus, the power of variable impedance control is made available to a wide variety of robotic systems and practical applications.

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.