State-of-the-art legged robots are either capable of measuring torque at the output of their drive systems, or have transparent drive systems which enable the computation of joint torques from motor currents. In either case, this sensor modality is seldom used in state estimation. In this paper, we propose to use joint torque measurements to estimate the centroidal states of legged robots. To do so, we project the whole-body dynamics of a legged robot into the nullspace of the contact constraints, allowing expression of the dynamics independent of the contact forces. Using the constrained dynamics and the centroidal momentum matrix, we are able to directly relate joint torques and centroidal states dynamics. Using the resulting model as the process model of an Extended Kalman Filter (EKF), we fuse the torque measurement in the centroidal state estimation problem. Through real-world experiments on a quadruped robot executing different gaits, we demonstrate that the estimated centroidal states from our torque-based EKF drastically improve the recovery of these quantities compared to direct computation.

In the context of model-based reinforcement learning and control, a large number of methods for learning system dynamics have been proposed in recent years. The purpose of these learned models is to synthesize new control policies. An important open question is how robust current dynamics-learning methods are to shifts in the data distribution due to changes in the control policy. We present a real-robot dataset which allows to systematically investigate this question. This dataset contains trajectories of a 3 degrees-of-freedom (DOF) robot being controlled by a diverse set of policies. For comparison, we also provide a simulated version of the dataset. Finally, we benchmark a few widely-used dynamics-learning methods using the proposed dataset. Our results show that the iid test error of a learned model is not necessarily a good indicator of its accuracy under control policies different from the one which generated the training data. This suggests that it may be important to evaluate dynamics-learning methods in terms of their transfer performance, rather than only their iid error.

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.

This paper presents a generic and efficient approach to generate dynamically consistent motions for under-actuated systems like humanoid or quadruped robots. The main contribution is a walking pattern generator, able to compute a stable trajectory of the center of mass of the robot along with the angular momentum, for any given configuration of contacts (e.g. on uneven, sloppy or slippery terrain, or with closed-gripper). Unlike existing methods, our solver is fast enough to be applied as a model-predictive controller. We then integrate this pattern generator in a complete framework: an acyclic contact planner is first used to automatically compute the contact sequence from a 3D model of the environment and a desired final posture; a stable walking pattern is then computed by the proposed solver; a dynamically-stable whole-body trajectory is finally obtained using a second-order hierarchical inverse kinematics. The implementation of the whole pipeline is fast enough to plan a step while the previous one is executed. The interest of the method is demonstrated by real experiments on the HRP-2 robot, by performing long-step walking and climbing a staircase with handrail support.