The attention given to impedance control in recent years does not match a similar focus on the choice of impedance values that the controller should execute. Current methods are hardly general and often compute fixed controller gains relying on the use of expensive sensors. In this article, we address the problem of online impedance planning for Cartesian impedance controllers that do not assign the closed-loop inertia. We propose an optimization-based algorithm that, given the Cartesian inertia, computes the stiffness and damping gains without relying on force/torque measurements and so that the effects of perturbations are less than a maximum acceptable value. By doing so, we increase robot resilience to unexpected external disturbances while guaranteeing performance and robustness. The algorithm provides an analytical solution in the case of impedance-controlled robots with diagonally dominant inertia matrix. Instead, established numerical methods are employed to deal with the more common case of nondiagonally dominant inertia. Our work attempts to create a general impedance planning framework, which needs no additional hardware and is easily applicable to any robotic system. Through experiments on real robots, including a quadruped and a robotic arm, our method is shown to be employable in real time and to lead to satisfactory behaviors.

Embedding elastic elements into legged robots through mechanical design enables highly efficient oscillating patterns that resemble natural gaits. However, current trajectory planning techniques miss the opportunity of taking advantage of these natural motions. This work proposes a locomotion planning method that aims to unify traditional trajectory generation with modal oscillations. Our method utilizes task-space linearized modes for generating center of mass trajectories on the sagittal plane. We then use nonlinear optimization to find the gait timings that match these trajectories within the Divergent Component of Motion planning framework. This way, we can robustly translate the modes-aware centroidal motions into joint coordinates. We validate our approach with promising results and insights through experiments on a compliant quadrupedal robot.

The vast majority of state-of-the-art walking robots employ flat or ball feet for locomotion, presenting limitations while stepping on obstacles, slopes, or unstructured terrain. Moreover, traditional feet for quadrupeds lack sensing systems that are able to provide information about the environment and about the foot interaction with the surroundings. This further diminishes their value. Inspired by our previous work on soft feet for bipedal robots, we present the SoftFoot-Q, an articulated adaptive foot for quadrupeds. This device is conceived to be robust and able to overcome the limitations of currently employed feet. The core idea behind our adaptive foot design is first introduced and validated through a simplified mathematical formulation of the problem. Subsequently, we present the chosen mechanical implementation to attempt overcoming current limitations. The realized prototype of adaptive foot is integrated and tested on the compliantly actuated quadrupedal robot ANYmal together with an ROS-based real-time foot pose reconstruction software. Both extensive field tests and indoor experiments show noticeable performance improvements, in terms of reduced slippage of the robot, with respect to both flat and ball feet.

In this paper, we consider a problem of foothold selection for the quadrupedal robots equipped with compliant adaptive feet. Starting from a model of the foot we compute the quality of the potential footholds considering also kinematic constraints and collisions during evaluation. Since terrain assessment and constraints checking are computationally expensive we applied a Convolutional Neural Network (CNN) to evaluate the potential footholds on the elevation map. We propose an efficient strategy for data clustering and segmentation with CNN. The data for training the neural network is collected off-line but the inference works on-line when the robot walks on rough terrains and allows for efficient adaptation to the terrain and exploitation of the properties of the soft adaptive feet.