This paper presents the first successful experiment implementing whole-body model predictive control with state feedback on a torque-control humanoid robot. We demonstrate that our control scheme is able to do whole-body target tracking, control the balance in front of strong external perturbations and avoid collision with an external object. The key elements for this success are threefold. First, optimal control over a receding horizon is implemented with Crocoddyl, an optimal control library based on differential dynamics programming, providing state-feedback control in less than 10 ms. Second, a warm start strategy based on memory of motion has been implemented to overcome the sensitivity of the optimal control solver to initial conditions. Finally, the optimal trajectories are executed by a low-level torque controller, feedbacking on direct torque measurement at high frequency. This paper provides the details of the method, along with analytical benchmarks with the real humanoid robot Talos.A video of the experiment is available at https://peertube.laas.fr/videos/watch/cbc25927-337c-4635-a1bc-153b9aeb4135

The lack of computational power on mobile robots is a well-known challenge when it comes to implementing a realtime MPC scheme to perform complex motions. Currently the best solvers are barely able to reach 100Hz for computing the control of a whole-body legged model, while modern robots are expecting new torque references in less than 1ms. This problem is usually tackled by using a handcrafted low-level tracking control whose inputs are the low-frequency trajectory computed by the MPC. We show that a linear state feedback controller naturally arises from the optimal control formulation and can be used directly in the low-level control loop along with other sensitivities of relevant time-varying parameters of the problem. When the optimal control problem is solved by DDP, this linear controller can be computed for cheap as a by-product of the backward pass, and corresponds in part to the classical Riccati gains. A side effect of our proposition is to show that Riccati gains are valuable assets that must be used to achieve an efficient control and that they are not stiffer than the optimal control scheme itself. We propose a complete implementation of this idea on a full-scale humanoid robot and demonstrate its importance with real experiments on the robot Talos.

When a big and heavy robot moves, it exerts large forces on the environment and on its own structure, its angular momentum can vary substantially, and even the robot's structure can deform if there is a mechanical weakness. Under these conditions, standard locomotion controllers can fail easily. In this article, we propose a complete control scheme to work with heavy robots in torque control. The full centroidal dynamics is used to generate walking gaits online, link deflections are taken into account to estimate the robot posture and all postural instructions are designed to avoid conflicting with each other, improving balance. These choices reduce model and control errors, allowing our centroidal stabilizer to compensate for the remaining residual errors. The stabilizer and motion generator are designed together to ensure feasibility under the assumption of bounded errors. We deploy this scheme to control the locomotion of the humanoid robot Talos, whose hip links flex when walking. It allows us to reach steps of 35 cm, for an average speed of 25 cm/sec, which is among the best performances so far for torque-controlled electric robots.

Locomotion of biped robots requires predictive controllers due to its unstable dynamics and physical limitations of contact forces. A real-time controller designed to perform complex motions while maintaining balance over feet must generate whole-body trajectories, predicting a few seconds in the future with a high enough updating rate to reduce model errors. Due to the huge computational power demanded by such solvers, future trajectories are usually generated using a reduced order model that contains the unstable dynamics. However, this simplification introduces feasibility problems on many edge cases. Considering the permanent improvement of computers and algorithms, whole-body locomotion in realtime is becoming a viable option for humanoids, and this article aims at illustrating this point. We propose a whole-body model predictive control scheme based on differential dynamic programming that takes into account the full dynamics of the system and decides the optimal actuation for the robot's lower body (20 degrees of freedom) along a preview horizon of 1.5 s. Our experimental validation on the torque-controlled robot Talos shows good and promising results for dynamic locomotion at different gaits as well as 10 cm height stairstep crossing.