Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019

Sensitivity of Legged Balance Control to Uncertainties and Sampling Period

We propose to quantify the effect of sensor and actuator uncertainties on the control of the center of mass and center of pressure in legged robots, since this is central for maintaining their balance with a limited support polygon. Our approach is based on robust control theory, considering uncertainties that can take any value between specified bounds. This provides a principled approach to deciding optimal feedback gains. Surprisingly, our main observation is that the sampling period can be as long as 200 ms with literally no impact on maximum tracking error and, as a result, on the guarantee that balance can be maintained safely. Our findings are validated in simulations and experiments with the torquecontrolled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless equally to biped and quadruped robots

Sensitivity of Legged Balance Control to Uncertainties and Sampling Period

We propose to quantify the effect of sensor and actuator uncertainties on the control of the center of mass and center of pressure in legged robots, since this is central for maintaining their balance with a limited support polygon. Our approach is based on robust control theory, considering uncertainties that can take any value between specified bounds. This provides a principled approach to deciding optimal feedback gains. Surprisingly, our main observation is that the sampling period can be as long as 200 ms with literally no impact on maximum tracking error and, as a result, on the guarantee that balance can be maintained safely. Our findings are validated in simulations and experiments with the torquecontrolled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless equally to biped and quadruped robots

Recent Progress in Legged Robots Locomotion Control

International audiencePurpose of review. In recent years, legged robots locomotion has been transitioning from mostly flat ground in controlled settings to generic indoor and outdoor environments, approaching now real industrial scenarios. This paper aims at documenting some of the key progress made in legged locomotion control that enabled this transition. Recent findings. Legged locomotion control makes extensive use of numerical trajectory optimization and its online implementation, Model Predictive Control. A key progress has been how this optimization is handled, with refined models and refined numerical methods. This led the legged locomotion research community to heavily invest in and contribute to the development of new optimization methods and efficient numerical software

Experimental Evaluation of Simple Estimators for Humanoid Robots

International audienceThis paper introduces and evaluates a family of new simple estimators to reconstruct the pose and velocity of the floating base. The estimation of the floating-base state is a critical challenge to whole-body control methods that rely on full-state information in high-rate feedback. Although the kinematics of grounded limbs may be used to estimate the pose and velocity of the body, modelling errors from ground irregularity, foot slip, and structural flexibilities limit the utility of estimation from kinematics alone. These difficulties have motivated the development of sensor fusion methods to augment body-mounted IMUs with kinematic measurements. Existing methods often rely on extended Kalman filtering, which lack convergence guarantees and may present difficulties in tuning. This paper proposes two new simplifications to the floating-base state estimation problem that make use of robust off-the-shelf orientation estimators to bootstrap development. Experiments for in-place balance and walking with the HRP-2 show that the simplifications yield results on par with the accuracy reported in the literature for other methods. As further benefits, the structure of the proposed estimators prevents divergence of the estimates, simplifies tuning, and admits efficient computation. These benefits are envisioned to help accelerate the development of baseline estimators in future humanoids