In the literature about model predictive control (MPC), contact forces are planned rather than controlled. In this paper, we propose a novel paradigm to incorporate effort measurements into a predictive controller, hence allowing to control them by direct measurement feedback. We first demonstrate why the classical optimal control formulation, based on position and velocity state feedback, cannot handle direct feedback on force information. Following previous approaches in force control, we then propose to augment the classical formulations with a model of the robot actuation, which naturally allows to generate online trajectories that adapt to sensed position, velocity and torques. We propose a complete implementation of this idea on the upper part of a real humanoid robot, and show through hardware experiments that this new formulation incorporating effort feedback outperforms classical MPC in challenging tasks where physical interaction with the environment is crucial.

The combinatorics inherent to the issue of planning legged locomotion can be addressed by decomposing the problem: first, select a guide path abstracting the contacts with a heuristic model; then compute the contact sequence to balance the robot gait along the guide path. While several models have been proposed to compute such a path, none have yet managed to efficiently capture the complexity of legged locomotion on arbitrary terrain. In this paper, we present a novel method to automatically build a local controller, or steering method, to generate a guide path along which a feasible contact sequence can be built. Our reinforcement learning approach is coupled with a geometric condition for feasibility during the training, which improves the convergence rate without incurring a loss in generality. We have designed a dedicated environment along with an associated reward function to run a classical reinforcement learning algorithm that computes the steering method. The policy takes a target velocity and a local heightmap of the terrain around the robot as inputs, and steers the path where new contacts should be created. It is then coupled with a contact generator that creates the contacts to support the robot movement. We show that the trained policy has an improved generalization and higher success rate at generating feasible contact plans than previous approaches. As a result, this policy can be used with a path planning algorithm to navigate complex environments.

As locomotion decisions must be taken by considering the future, most existing quadruped controllers are based on a model predictive controller (MPC) with a reduced model of the dynamics to generate the motion and a whole- body controller to execute it. Yet the simplifying assumptions of the MPC are often chosen ad-hoc or by intuition. In this article, we focus on a set of MPCs and analyze the effect of chosen model reductions on the behavior of the robot. Based on existing formulations, we present additional controllers to better understand the influence of model reductions on the controller capabilities. Finally, we propose a robust predictive controller capable of optimizing the foot placements, gait period, center- of-mass trajectory and ground reaction forces. The behavior of these controllers is statistically evaluated in simulation. This empirical study aims to assess the relative importance of the components of the optimal control problem (variables, costs, dynamics) to be able to take reasoned decisions instead of arbitrarily emphasizing or neglecting some of them. We also provide a qualitative study in simulation and on the real robot Solo-12.

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

We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, exploitation of the problem structure, and data sharing. It employs differential geometry to properly describe the state of any geometrical system, e.g. floating-base systems. Additionally, we propose a novel optimal control algorithm called Feasibility-driven Differential Dynamic Programming (FDDP). Our method does not add extra decision variables which often increases the computation time per iteration due to factorization. FDDP shows a greater globalization strategy compared to classical Differential Dynamic Programming (DDP) algorithms. Concretely, we propose two modifications to the classical DDP algorithm. First, the backward pass accepts infeasible state-control trajectories. Second, the rollout keeps the gaps open during the early "exploratory" iterations (as expected in multipleshooting methods with only equality constraints). We showcase the performance of our framework using different tasks. With our method, we can compute highly-dynamic maneuvers (e.g. jumping, front-flip) within few milliseconds.

We present an optimization framework for the design and analysis of underactuated biped walkers, characterized by passive or actuated joints with rigid or non-negligible elastic actuation/transmission elements. The framework is based on optimal control, dealing with geometric constraints and various dynamic objective functions, as well as boundary conditions, which helps in selecting optimal values both for the actuation and the transmission parameters. Solutions of the formulated problems are shown for different kinds of bipedal architectures, and comparisons drawn between traditional rigid robots and compliant ones show the energy-efficiency of compliant actuators in the context of locomotion.

transHumUs is an artistic work recently exhibited at the 56th Venice Biennale. The work aims at freeing trees from their roots. How to translate this poetic ambition into technological terms? This paper reports on the setup and the implementation of the project. It shows how state of the art mobile robotics technology can contribute to contemporary art development. The challenge has been to design original mobile platforms carrying charges of three tones, while moving noiseless according to tree metabolism, in operational spaces populated by visitors.