Ahmad Gazar

Shahram Khorshidi, Ahmad Gazar, Nicholas Rotella et al.

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 with 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.

Ahmad Gazar, Majid Khadiv, Andrea Del Prete et al.

Linear Model Predictive Control (MPC) has been successfully used for generating feasible walking motions for humanoid robots. However, the effect of uncertainties on constraints satisfaction has only been studied using Robust MPC (RMPC) approaches, which account for the worst-case realization of bounded disturbances at each time instant. In this letter, we propose for the first time to use linear stochastic MPC (SMPC) to account for uncertainties in bipedal walking. We show that SMPC offers more flexibility to the user (or a high level decision maker) by tolerating small (user-defined) probabilities of constraint violation. Therefore, SMPC can be tuned to achieve a constraint satisfaction probability that is arbitrarily close to 100\%, but without sacrificing performance as much as tube-based RMPC. We compare SMPC against RMPC in terms of robustness (constraint satisfaction) and performance (optimality). Our results highlight the benefits of SMPC and its interest for the robotics community as a powerful mathematical tool for dealing with uncertainties.

Ahmad Gazar, Gabriele Nava, Francisco Javier Andrade Chavez et al.

Nonlinear controllers for floating base systems in contact with the environment are often framed as quadratic programming (QP) optimization problems. Common drawbacks of such QP based controllers are: the control input often experiences discontinuities; no force feedback from Force/Torque (FT) sensors installed on the robot is taken into account. This paper attempts to address these limitations using jerk based control architectures. The proposed controllers assume the rate-of-change of the joint torques as control input, and exploit the system position, velocity, accelerations, and contact wrenches as measurable quantities. The key ingredient of the presented approach is a one-to-one correspondence between free variables and an inner approximation of the manifold defined by the contact stability constraints. More precisely, the proposed correspondence covers completely the contact stability manifold except for the so-called friction cone, for which there exists a unique correspondence for more than 90% of its elements. The correspondence allows us to transform the underlying constrained optimisation problem into one that is unconstrained. Then, we propose a jerk control framework that exploits the proposed correspondence and uses FT measurements in the control loop. Furthermore, we present Lyapunov stable controllers for the system momentum in the jerk control framework. The approach is validated with simulations and experiments using the iCub humanoid robot.