Michael Bloesch

State Estimation for Legged Robots - Consistent Fusion of Leg Kinematics and IMU

This paper introduces a state estimation framework for legged robots that allows estimating the full pose of the robot without making any assumptions about the geometrical structure of its environment. This is achieved by means of an Observability Constrained Extended Kalman Filter that fuses kinematic encoder data with on-board IMU measurements. By including the absolute position of all footholds into the filter state, simple model equations can be formulated which accurately capture the uncertainties associated with the intermittent ground contacts. The resulting filter simultaneously estimates the position of all footholds and the pose of the main body. In the algorithmic formulation, special attention is paid to the consistency of the linearized filter: it maintains the same observability properties as the nonlinear system, which is a prerequisite for accurate state estimation. The presented approach is implemented in simulation and validated experimentally on an actual quadrupedal robot.

Quadrupedal locomotion using hierarchical operational space control

This paper presents the application of operational space control based on hierarchical task optimization for quadrupedal locomotion. We show how the behavior of a complex robotic machine can be described by a simple set of least squares problems with different priorities for motion, torque, and force optimization. Using projected dynamics of floating base systems with multiple contact points, the optimization dimensionality can be reduced or decoupled such that the formulation is purely based on the inversion of kinematic system properties. The present controller is extensively tested in various experiments using the fully torque controllable quadrupedal robot StarlETH. The load distribution is optimized for static walking gaits to improve contact stability and/or actuator efficiency under various terrain conditions. This is augmented with simultaneous joint position and torque limitations as well as with an interpolation method to ensure smooth contact transitions. The same control structure is further used to stabilize dynamic trotting gaits under significant external disturbances such as uneven ground or pushes. To the best of our knowledge, this work is the first documentation of static and dynamic locomotion with pure task-space inverse dynamics (no joint position feedback) control.

State estimation for a humanoid robot

This paper introduces a framework for state estimation on a humanoid robot platform using only common proprioceptive sensors and knowledge of leg kinematics. The presented approach extends that detailed in prior work on a point-foot quadruped platform by adding the rotational constraints imposed by the humanoids flat feet. As in previous work, the proposed Extended Kalman Filter accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. A nonlinear observability analysis is performed on both the point-foot and flat-foot filters and it is concluded that the addition of rotational constraints significantly simplifies singular cases and improves the observability characteristics of the system. Results on a simulated walking dataset demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.

State estimation for legged robots on unstable and slippery terrain

This paper presents a state estimation approach for legged robots based on stochastic filtering. The key idea is to extract information from the kinematic constraints given through the intermittent contacts with the ground and to fuse this information with inertial measurements. To this end, we design an unscented Kalman filter based on a consistent formulation of the underlying stochastic model. To increase the robustness of the filter, an outliers rejection methodology is included into the update step. Furthermore, we present the nonlinear observability analysis of the system, where, by considering the special nature of 3D rotations, we obtain a relatively simple form of the corresponding observability matrix. This yields, that, except for the global position and the yaw angle, all states are in general observable. This also holds if only one foot is in contact with the ground. The presented filter is evaluated on a real quadruped robot trotting over an uneven and slippery terrain.

gvnn: neural network library for geometric computer vision

We introduce gvnn, a neural network library in Torch aimed towards bridging the gap between classic geometric computer vision and deep learning. Inspired by the recent success of Spatial Transformer Networks, we propose several new layers which are often used as parametric transformations on the data in geometric computer vision. These layers can be inserted within a neural network much in the spirit of the original spatial transformers and allow backpropagation to enable end-to-end learning of a network involving any domain knowledge in geometric computer vision. This opens up applications in learning invariance to 3D geometric transformation for place recognition, end-to-end visual odometry, depth estimation and unsupervised learning through warping with a parametric transformation for image reconstruction error.

Dense visual-inertial navigation system for mobile robots

Real-time dense mapping and pose estimation is essential for a wide range of navigation tasks in mobile robotic applications. We propose an odometry and mapping system that leverages the full photometric information from a stereo-vision system as well as inertial measurements in a probabilistic framework while running in real-time on a single low-power Intel CPU core. Instead of performing mapping and localization on a set of sparse image features, we use the complete dense image intensity information in our navigation system. By incorporating a probabilistic model of the stereo sensor and the IMU, we can robustly estimate the ego-motion as well as a dense 3D model of the environment in real-time. The probabilistic formulation of the joint odometry estimation and mapping process enables to efficiently reject temporal outliers in ego-motion estimation as well as spatial outliers in the mapping process. To underline the versatility of the proposed navigation system, we evaluate it in a set of experiments on a multi-rotor system as well as on a quadrupedal walking robot. We tightly integrate our framework into the stabilization-loop of the UAV and the mapping framework of the walking robot. It is shown that the dense framework exhibits good tracking and mapping performance in terms of accuracy as well as robustness in scenarios with highly dynamic motion patterns while retaining a relatively small computational footprint. This makes it an ideal candidate for control and navigation tasks in unstructured GPS-denied environments, for a wide range of robotic platforms with power and weight constraints. The proposed framework is released as an open-source ROS package.

Practice Makes Perfect: An Optimization-Based Approach to Controlling Agile Motions for a Quadruped Robot

This article approaches the problem of controlling quadrupedal running and jumping motions with a parameterized, model-based, state-feedback controller. Inspired by the motor learning principles observed in nature, our method automatically fine tunes the parameters of our controller by repeatedly executing slight variations of the same motion task. This learn-through-practice process is performed in simulation to best exploit computational resources and to prevent the robot from damaging itself. To ensure that the simulation results match the behavior of the hardware platform, we introduce and validate an accurate model of the compliant actuation system. The proposed method is experimentally verified on the torque-controllable quadruped robot StarlETH by executing squat jumps and dynamic gaits, such as a running trot, pronk, and a bounding gait.

Unsupervised identification and prediction of foothold robustness

This paper addresses the problem of evaluating and estimating the mechanical robustness of footholds for legged robots in unstructured terrain. In contrast to approaches that rely on human expert knowledge or human defined criteria to identify appropriate footholds, our method uses the robot itself to assess whether a certain foothold is adequate or not. To this end, one of the robots legs is employed to haptically explore an unknown foothold. The robustness of the foothold is defined by a simple metric as a function of the achievable ground reaction forces. This haptic feedback is associated with the foothold shape to estimate the robustness of untouched footholds. The underlying shape clustering principles are tested on synthetic data and in hardware experiments using a single-leg testbed.

Quadrupedal robots with stiff and compliant actuation

Abstract In the broader context of quadrupedal locomotion, this overview article introduces and compares two platforms that are similar in structure, size, and morphology, yet differ greatly in their concept of actuation. The first, ALoF, is a classically stiff actuated robot that is controlled kinematically, while the second, StarlETH, uses a soft actuation scheme based on Changedhighly compliant series elastic actuators. We show how this conceptual difference influences design and control of the robots, compare the hardware of the two systems, and show exemplary their advantages in different applications. Zusammenfassung Der vorliegende Beitrag vergleicht zwei Laufroboter, die sich in Hinblick auf Struktur, Größe und Morphologie stark ähneln, jedoch im Antriebskonzept klar unterscheiden. Während es sich beim ersten System, ALoF, um einen klassisch angetriebenen Roboter handelt der kinematisch geregelt wird, besitzt der zweite Roboter, StarlETH, Federelemente im Antriebsstrang. Diese ermöglichen eine weiche, kraftgeregelte Aktuierung. Der Beitrag zeigt wie dieser Unterschied Design und Regelung der Roboter beeinflusst, vergleicht die Hardware und erläutert Vor- und Nachteile in verschiedenen Anwendungsfällen.

Unified state estimation for a ballbot

This paper presents a method for state estimation on a ballbot; i.e., a robot balancing on a single sphere. Within the framework of an extended Kalman filter and by utilizing a complete kinematic model of the robot, sensory information from different sources is combined and fused to obtain accurate estimates of the robots attitude, velocity, and position. This information is to be used for state feedback control of the dynamically unstable system. Three incremental encoders (attached to the omniwheels that drive the ball of the robot) as well as three rate gyroscopes and accelerometers (attached to the robots main body) are used as sensors. For the presented method, observability is proven analytically for all essential states in the system, and the algorithm is experimentally evaluated on the Ballbot Rezero.