Online Optimal Impedance Planning for Legged Robots Real world applications require robots to operate in unstructured environments. This kind of scenarios may lead to unexpected environmental contacts or undesired interactions, which may harm people or impair the robot. Adjusting the behavior of the system through impedance control techniques is an effective solution to these problems. However, selecting an adequate impedance is not a straightforward process. Normally, robot users manually tune the controller gains with trial and error methods. This approach is generally slow and requires practice. Moreover, complex tasks may require different impedance during different phases of the task. This paper introduces an optimization algorithm for online planning of the Cartesian robot impedance to adapt to changes in the task, robot configuration, expected disturbances, external environment and desired performance, without employing any direct force measurements. We provide an analytical solution leveraging the massspringdamper behavior that is conferred to the robot body by the Cartesian impedance controller. Stability during gains variation is also guaranteed. The effectiveness of the method is experimentally validated on the quadrupedal robot ANYmal. The variable impedance helps the robot to tackle challenging scenarios like walking on rough terrain and colliding with an obstacle.

First Steps Towards Full Model Based Motion Planning and Control of Quadrupeds: A Hybrid Zero Dynamics Approach The hybrid zero dynamics (HZD) approach has become a powerful tool for the gait planning and control of bipedal robots. This paper aims to extend the HZD methods to address walking, ambling and trotting behaviors on a quadrupedal robot. We present a framework that systematically generates a wide range of optimal trajectories and then provably stabilizes them for the fullorder, nonlinear and hybrid dynamical models of quadrupedal locomotion. The gait planning is addressed through a scalable nonlinear programming using direct collocation and HZD. The controller synthesis for the exponential stability is then achieved through the Poincare sections analysis. In particular, we employ an iterative optimization algorithm involving linear and bilinear matrix inequalities (LMIs and BMIs) to design HZDbased controllers that guarantee the exponential stability of the fixed points for the Poincare return map. The power of the framework is demonstrated through gait generation and HZDbased controller synthesis for an advanced quadruped robot, xe2x80x94Vision 60, with 36 state variables and 12 control inputs. The numerical simulations as well as real world experiments confirm the validity of the proposed framework.