arXiv subjects

Stefan Schaal

Publications and source records attributed to Stefan Schaal.

At least 73 records · Page 4Linked to original sources

arXiv2016

Probabilistic Articulated Real-Time Tracking for Robot Manipulation

We propose a probabilistic filtering method which fuses joint measurements with depth images to yield a precise, real-time estimate of the end-effector pose in the camera frame. This avoids the need for frame transformations when using it in combination with visual object tracking methods. Precision is achieved by modeling and correcting biases in the joint measurements as well as inaccuracies in the robot model, such as poor extrinsic camera calibration. We make our method computationally efficient through a principled combination of Kalman filtering of the joint measurements and asynchronous depth-image updates based on the Coordinate Particle Filter. We quantitatively evaluate our approach on a dataset recorded from a real robotic platform, annotated with ground truth from a motion capture system. We show that our approach is robust and accurate even under challenging conditions such as fast motion, significant and long-term occlusions, and time-varying biases. We release the dataset along with open-source code of our approach to allow for quantitative comparison with alternative approaches.

cs.RO↗

arXiv2016

Stepping Stabilization Using a Combination of DCM Tracking and Step Adjustment

In this paper, a method for stabilizing biped robots stepping by a combination of Divergent Component of Motion (DCM) tracking and step adjustment is proposed. In this method, the DCM trajectory is generated, consistent with the predefined footprints. Furthermore, a swing foot trajectory modification strategy is proposed to adapt the landing point, using DCM measurement. In order to apply the generated trajectories to the full robot, a Hierarchical Inverse Dynamics (HID) is employed. The HID enables us to use different combinations of the DCM tracking and step adjustment for stabilizing different biped robots. Simulation experiments on two scenarios for two different simulated robots, one with active ankles and the other with passive ankles, are carried out. Simulation results demonstrate the effectiveness of the proposed method for robots with both active and passive ankles.

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arXiv2016

DOOMED: Direct Online Optimization of Modeling Errors in Dynamics

It has long been hoped that model-based control will improve tracking performance while maintaining or increasing compliance. This hope hinges on having or being able to estimate an accurate inverse dynamics model. As a result, substantial effort has gone into modeling and estimating dynamics (error) models. Most recent research has focused on learning the true inverse dynamics using data points mapping observed accelerations to the torques used to generate them. Unfortunately, if the initial tracking error is bad, such learning processes may train substantially off-distribution to predict well on actual observed acceleration rather then the desired accelerations. This work takes a different approach. We define a class of gradient-based online learning algorithms we term Direct Online Optimization for Modeling Errors in Dynamics (DOOMED) that directly minimize an objective measuring the divergence between actual and desired accelerations. Our objective is defined in terms of the true system's unknown dynamics and is therefore impossible to evaluate. However, we show that its gradient is measurable online from system data. We develop a novel adaptive control approach based on running online learning to directly correct (inverse) dynamics errors in real time using the data stream from the robot to accurately achieve desired accelerations during execution.

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arXiv2016

A Convex Model of Momentum Dynamics for Multi-Contact Motion Generation

Linear models for control and motion generation of humanoid robots have received significant attention in the past years, not only due to their well known theoretical guarantees, but also because of practical computational advantages. However, to tackle more challenging tasks and scenarios such as locomotion on uneven terrain, a more expressive model is required. In this paper, we are interested in contact interaction-centered motion optimization based on the momentum dynamics model. This model is non-linear and non-convex; however, we find a relaxation of the problem that allows us to formulate it as a single convex quadratically-constrained quadratic program (QCQP) that can be very efficiently optimized. Furthermore, experimental results suggest that this relaxation is tight and therefore useful for multi-contact planning. This convex model is then coupled to the optimization of end-effector contacts location using a mixed integer program, which can be solved in realtime. This becomes relevant e.g. to recover from external pushes, where a predefined stepping plan is likely to fail and an online adaptation of the contact location is needed. The performance of our algorithm is demonstrated in several multi-contact scenarios for humanoid robot.

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arXiv2016

Robust Gaussian Filtering using a Pseudo Measurement

Many sensors, such as range, sonar, radar, GPS and visual devices, produce measurements which are contaminated by outliers. This problem can be addressed by using fat-tailed sensor models, which account for the possibility of outliers. Unfortunately, all estimation algorithms belonging to the family of Gaussian filters (such as the widely-used extended Kalman filter and unscented Kalman filter) are inherently incompatible with such fat-tailed sensor models. The contribution of this paper is to show that any Gaussian filter can be made compatible with fat-tailed sensor models by applying one simple change: Instead of filtering with the physical measurement, we propose to filter with a pseudo measurement obtained by applying a feature function to the physical measurement. We derive such a feature function which is optimal under some conditions. Simulation results show that the proposed method can effectively handle measurement outliers and allows for robust filtering in both linear and nonlinear systems.

stat.ML↗

arXiv2016

On the Fundamental Importance of Gauss-Newton in Motion Optimization

Hessian information speeds convergence substantially in motion optimization. The better the Hessian approximation the better the convergence. But how good is a given approximation theoretically? How much are we losing? This paper addresses that question and proves that for a particularly popular and empirically strong approximation known as the Gauss-Newton approximation, we actually lose very little--for a large class of highly expressive objective terms, the true Hessian actually limits to the Gauss-Newton Hessian quickly as the trajectory's time discretization becomes small. This result both motivates it's use and offers insight into computationally efficient design. For instance, traditional representations of kinetic energy exploit the generalized inertia matrix whose derivatives are usually difficult to compute. We introduce here a novel reformulation of rigid body kinetic energy designed explicitly for fast and accurate curvature calculation. Our theorem proves that the Gauss-Newton Hessian under this formulation efficiently captures the kinetic energy curvature, but requires only as much computation as a single evaluation of the traditional representation. Additionally, we introduce a technique that exploits these ideas implicitly using Cholesky decompositions for some cases when similar objective terms reformulations exist but may be difficult to find. Our experiments validate these findings and demonstrate their use on a real-world motion optimization system for high-dof motion generation.

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arXiv2016

Automatic LQR Tuning Based on Gaussian Process Global Optimization

This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four-dimensional tuning problems highlight the method's potential for automatic controller tuning on robotic platforms.

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arXiv2016

Depth-Based Object Tracking Using a Robust Gaussian Filter

We consider the problem of model-based 3D-tracking of objects given dense depth images as input. Two difficulties preclude the application of a standard Gaussian filter to this problem. First of all, depth sensors are characterized by fat-tailed measurement noise. To address this issue, we show how a recently published robustification method for Gaussian filters can be applied to the problem at hand. Thereby, we avoid using heuristic outlier detection methods that simply reject measurements if they do not match the model. Secondly, the computational cost of the standard Gaussian filter is prohibitive due to the high-dimensional measurement, i.e. the depth image. To address this problem, we propose an approximation to reduce the computational complexity of the filter. In quantitative experiments on real data we show how our method clearly outperforms the standard Gaussian filter. Furthermore, we compare its performance to a particle-filter-based tracking method, and observe comparable computational efficiency and improved accuracy and smoothness of the estimates.

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arXiv2016

Inertial Sensor-Based Humanoid Joint State Estimation

This work presents methods for the determination of a humanoid robot's joint velocities and accelerations directly from link-mounted Inertial Measurement Units (IMUs) each containing a three-axis gyroscope and a three-axis accelerometer. No information about the global pose of the floating base or its links is required and precise knowledge of the link IMU poses is not necessary due to presented calibration routines. Additionally, a filter is introduced to fuse gyroscope angular velocities with joint position measurements and compensate the computed joint velocities for time-varying gyroscope biases. The resulting joint velocities are subject to less noise and delay than filtered velocities computed from numerical differentiation of joint potentiometer signals, leading to superior performance in joint feedback control as demonstrated in experiments performed on a SARCOS hydraulic humanoid.

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arXiv2015

Momentum Control with Hierarchical Inverse Dynamics on a Torque-Controlled Humanoid

Hierarchical inverse dynamics based on cascades of quadratic programs have been proposed for the control of legged robots. They have important benefits but to the best of our knowledge have never been implemented on a torque controlled humanoid where model inaccuracies, sensor noise and real-time computation requirements can be problematic. Using a reformulation of existing algorithms, we propose a simplification of the problem that allows to achieve real-time control. Momentum-based control is integrated in the task hierarchy and a LQR design approach is used to compute the desired associated closed-loop behavior and improve performance. Extensive experiments on various balancing and tracking tasks show very robust performance in the face of unknown disturbances, even when the humanoid is standing on one foot. Our results demonstrate that hierarchical inverse dynamics together with momentum control can be efficiently used for feedback control under real robot conditions.

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arXiv2015

Humanoid Momentum Estimation Using Sensed Contact Wrenches

This work presents approaches for the estimation of quantities important for the control of the momentum of a humanoid robot. In contrast to previous approaches which use simplified models such as the Linear Inverted Pendulum Model, we present estimators based on the momentum dynamics of the robot. By using this simple yet dynamically-consistent model, we avoid the issues of using simplified models for estimation. We develop an estimator for the center of mass and full momentum which can be reformulated to estimate center of mass offsets as well as external wrenches applied to the robot. The observability of these estimators is investigated and their performance is evaluated in comparison to previous approaches.

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arXiv2015

Trajectory generation for multi-contact momentum-control

Simplified models of the dynamics such as the linear inverted pendulum model (LIPM) have proven to perform well for biped walking on flat ground. However, for more complex tasks the assumptions of these models can become limiting. For example, the LIPM does not allow for the control of contact forces independently, is limited to co-planar contacts and assumes that the angular momentum is zero. In this paper, we propose to use the full momentum equations of a humanoid robot in a trajectory optimization framework to plan its center of mass, linear and angular momentum trajectories. The model also allows for planning desired contact forces for each end-effector in arbitrary contact locations. We extend our previous results on LQR design for momentum control by computing the (linearized) optimal momentum feedback law in a receding horizon fashion. The resulting desired momentum and the associated feedback law are then used in a hierarchical whole body control approach. Simulation experiments show that the approach is computationally fast and is able to generate plans for locomotion on complex terrains while demonstrating good tracking performance for the full humanoid control.

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arXiv2015

A New Perspective and Extension of the Gaussian Filter

The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF from a variational-inference perspective. We analyse how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.

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arXiv2015

Policy Learning with Hypothesis based Local Action Selection

For robots to be able to manipulate in unknown and unstructured environments the robot should be capable of operating under partial observability of the environment. Object occlusions and unmodeled environments are some of the factors that result in partial observability. A common scenario where this is encountered is manipulation in clutter. In the case that the robot needs to locate an object of interest and manipulate it, it needs to perform a series of decluttering actions to accurately detect the object of interest. To perform such a series of actions, the robot also needs to account for the dynamics of objects in the environment and how they react to contact. This is a non trivial problem since one needs to reason not only about robot-object interactions but also object-object interactions in the presence of contact. In the example scenario of manipulation in clutter, the state vector would have to account for the pose of the object of interest and the structure of the surrounding environment. The process model would have to account for all the aforementioned robot-object, object-object interactions. The complexity of the process model grows exponentially as the number of objects in the scene increases. This is commonly the case in unstructured environments. Hence it is not reasonable to attempt to model all object-object and robot-object interactions explicitly. Under this setting we propose a hypothesis based action selection algorithm where we construct a hypothesis set of the possible poses of an object of interest given the current evidence in the scene and select actions based on our current set of hypothesis. This hypothesis set tends to represent the belief about the structure of the environment and the number of poses the object of interest can take. The agent's only stopping criterion is when the uncertainty regarding the pose of the object is fully resolved.

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arXiv2015

Probabilistic Depth Image Registration incorporating Nonvisual Information

In this paper, we derive a probabilistic registration algorithm for object modeling and tracking. In many robotics applications, such as manipulation tasks, nonvisual information about the movement of the object is available, which we will combine with the visual information. Furthermore we do not only consider observations of the object, but we also take space into account which has been observed to not be part of the object. Furthermore we are computing a posterior distribution over the relative alignment and not a point estimate as typically done in for example Iterative Closest Point (ICP). To our knowledge no existing algorithm meets these three conditions and we thus derive a novel registration algorithm in a Bayesian framework. Experimental results suggest that the proposed methods perform favorably in comparison to PCL implementations of feature mapping and ICP, especially if nonvisual information is available.

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arXiv2015

The Coordinate Particle Filter - A novel Particle Filter for High Dimensional Systems

Parametric filters, such as the Extended Kalman Filter and the Unscented Kalman Filter, typically scale well with the dimensionality of the problem, but they are known to fail if the posterior state distribution cannot be closely approximated by a density of the assumed parametric form. For nonparametric filters, such as the Particle Filter, the converse holds. Such methods are able to approximate any posterior, but the computational requirements scale exponentially with the number of dimensions of the state space. In this paper, we present the Coordinate Particle Filter which alleviates this problem. We propose to compute the particle weights recursively, dimension by dimension. This allows us to explore one dimension at a time, and resample after each dimension if necessary. Experimental results on simulated as well as real data confirm that the proposed method has a substantial performance advantage over the Particle Filter in high-dimensional systems where not all dimensions are highly correlated. We demonstrate the benefits of the proposed method for the problem of multi-object and robotic manipulator tracking.

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arXiv2015

Probabilistic Object Tracking using a Range Camera

We address the problem of tracking the 6-DoF pose of an object while it is being manipulated by a human or a robot. We use a dynamic Bayesian network to perform inference and compute a posterior distribution over the current object pose. Depending on whether a robot or a human manipulates the object, we employ a process model with or without knowledge of control inputs. Observations are obtained from a range camera. As opposed to previous object tracking methods, we explicitly model self-occlusions and occlusions from the environment, e.g, the human or robotic hand. This leads to a strongly non-linear observation model and additional dependencies in the Bayesian network. We employ a Rao-Blackwellised particle filter to compute an estimate of the object pose at every time step. In a set of experiments, we demonstrate the ability of our method to accurately and robustly track the object pose in real-time while it is being manipulated by a human or a robot.

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arXiv2014

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 [1] on a quadruped platform by incorporating the rotational constraints imposed by the humanoid's flat feet. As in previous work, the proposed Extended Kalman Filter (EKF) accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. The filter employs a sensor-based prediction model which uses inertial data from an IMU and corrects for integrated error using a kinematics-based measurement model which relies on joint encoders and a kinematic model to determine the relative position and orientation of the feet. A nonlinear observability analysis is performed on both the original and updated filters and it is concluded that the new filter significantly simplifies singular cases and improves the observability characteristics of the system. Results on simulated walking and squatting datasets demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.

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