Feasible Wrench Set Computation for Legged Robots

During locomotion, legged robots interact with the ground by sequentially establishing and breaking contact. The interaction wrenches that arise from contact are used to steer the robot's Center of Mass (CoM) and reject perturbations that make the system deviate from the desired trajectory and often make them fall. The feasibility of a given control target (desired CoM wrench or acceleration) is conditioned by the contact point distribution, ground friction, and actuation limits. In this work, we develop an algorithm to compute the set of feasible wrenches that a legged robot can exert on its CoM through contact. The presented method can be used with any amount of non-coplanar contacts and takes into account actuation limits and limitations based on an inelastic contact model with Coulomb friction. This is exemplified with a planar biped model standing with the feet at different heights. Exploiting assumptions from the contact model, we explain how to compute the set of wrenches that are feasible on the CoM when the contacts remain in position as well as the ones that are feasible when some of the contacts are broken. Therefore, this algorithm can be used to assess whether a switch in contact configuration is feasible while achieving a given control task. Furthermore, the method can be used to identify the directions in which the system is not actuated (i.e. a wrench cannot be exerted in those directions). We show how having a joint be actuated or passive can change the non-actuated wrench directions of a robot at a given pose using a spatial model of a lower-extremity exoskeleton. Therefore, this algorithm is also a useful tool for the design phase of the system. This work presents a useful tool for the control and design of legged systems that extends on the current state of the art.

A Device and Method to Identify Hip, Knee and Ankle Joint Impedance During Walking

Knowledge on joint impedance during walking in various conditions is relevant for clinical decision making and the development of robotic gait trainers, leg prostheses, leg orthotics, and wearable exoskeletons. Whereas ankle impedance during walking has been experimentally assessed, knee and hip joint impedance during walking have not been identified yet. Here we developed and evaluated a lower limb perturbator to identify hip, knee and ankle joint impedance during treadmill walking. The lower limb perturbator (LOPER) consists of an actuator connected to the thigh via rods. The LOPER allows to apply force perturbations to a free-hanging leg, while standing on the contralateral leg, with a bandwidth of up to 39Hz. While walking in minimal impedance mode, the interaction forces between LOPER and the thigh were low (<5N) and the effect on the walking pattern was smaller than the within-subject variability during normal walking. Using a non-linear multibody dynamical model of swing leg dynamics, the hip, knee and ankle joint impedance were estimated at three time points during the swing phase for nine subjects walking at a speed of 0.5 m/s. The identified model was well able to predict the experimental responses, since the mean variance accounted for was 99%, 96%, and 77%, for the hip, knee and ankle respectively. The averaged across subjects stiffness varied between the three time point within 34-66 Nm/rad, 0-3.5 Nm/rad, and 2.5-24 Nm/rad for the hip, knee and ankle joint respectively. The damping varied between 1.9-4.6 Nms/rad, 0.02-0.14 Nms/rad, and 0.2-2.4 Nms/rad for hip, knee, and ankle respectively. The developed LOPER has a negligible effect on the unperturbed walking pattern and allows to identify hip, knee and ankle joint impedance during the swing phase.