Tine Lefebvre

Kalman filters for non-linear systems: a comparison of performance

The Kalman filter is a well-known recursive state estimator for linear systems. In practice, the algorithm is often used for non-linear systems by linearizing the systems process and measurement models. Different ways of linearizing the models lead to different filters. In some applications, these ‘Kalman filter variants’ seem to perform well, while for other applications they are useless. When choosing a filter for a new application, the literature gives us little to rely on. This paper tries to bridge the gap between the theoretical derivation of a Kalman filter variant and its performance in practice when applied to a non-linear system, by providing an application-independent analysis of the performances of the common Kalman filter variants.  Correlated uncertainties can be dealt with by augmenting the state vector, this is the original formulation of the KF (Kalman 1960). Expressed in this new state vector, the process and measurement models are of the form (1) and (2) with uncorrelated uncertainties. This paper separates performance evaluation of Kalman filters into (i) consistency, and (ii) information content of the estimates; and it separates the filter structure into (i) the process update step, and (ii) the measurement update step. This decomposition provides the insights supporting an objective and systematic evaluation of the appropriateness of a particular Kalman filter variant in a particular application.

Estimating first-order geometric parameters and monitoring contact transitions during force controlled compliant motion

This paper uses (linearized) Kalman filters to estimate first-order geometric parameters (i.e., orientation of contact normals and location of contact points) that occur in force-controlled compliant motions. The time variance of these parameters is also estimated. In addition, transitions between contact situations can be monitored. The contact between the manipulated object and its environment is general, i.e., multiple contacts can occur at the same time, and both the topology and the geometry of each single contact are arbitrary. The two major theoretical contributions are 1) the integration of the general contact model, developed previously by the authors, into a state-space form suitable for recursive processing; and 2) the use of the reciprocity constraint between ideal contact forces and motion freedoms as the “measurement equation” of the Kalman filter. The theory is illustrated by full 3-D experiments. The approach of this paper allows a breakthrough in the state of the art dominated by the classical, orthogonal contact models of Mason that can only cope with a limited (albeit important) subset of all possible contact situations.

Active compliant motion: a survey

Whether they are asked to polish or assemble parts, clean the house or open doors, the future generation of robots will have to cope with contact tasks under uncertainty in a stable and safe manner. Obtaining a controlled contact motion under uncertainty is still a major challenge for the robotics community. At present most research groups focus on one of the subcomponents (i.e., modeling, planning, estimation or control) of the system, and no overall system is developed yet. This paper presents a literature survey of the state-of-the-art of the subcomponents and points to the need for effective integration of those components.

Bayesian Hybrid Model-State Estimation Applied to Simultaneous Contact Formation Recognition and Geometrical Parameter Estimation

In this paper we describe a Bayesian approach to model selection and state estimation for sensor-based robot tasks. The approach is illustrated with a hybrid model-state estimation example from force-controlled autonomous compliant motion: simultaneous (discrete) contact formation recognition and estimation of (continuous) geometrical parameters. Previous research in this area mostly tries to solve one of the two subproblems, or treats the contact formation recognition problem separately, avoiding integration between the solutions to the contact formation recognition and the geometrical parameter estimation problems. A more powerful hybrid model, explicitly modeling contact formation transitions, is developed to deal with larger uncertainties. This paper demonstrates that Kalman filter variants have limits: iterated extended Kalman filters can only handle small uncertainties on the geometrical parameters, while the non-minimal state Kalman filter cannot deal with model selection. Particle filters can handle the increased level of model complexity. Explicit measurement equations for the particle filter are derived from the implicit kinematic and energetic constraints. The experiments prove that the particle filter approach successfully estimates the hybrid joint posterior density of the discrete contact formation variable and the 12-dimensional, continuous geometrical parameter vector during the execution of an assembly task. The problem shows similarities with the well-known problems of data association in simultaneous localization and map-building (SLAM) and model selection in global localization.

Nonlinear Kalman filtering for force-controlled robot tasks

Introduction.- Literature Survey: Autonomous Compliant Motion.- Literature Survey: Bayesian Probability Theory.- Kalman Filters for Nonlinear Systems.- The Non-Minimal State Kalman Filter.- Contact Modelling.- Geometrical Parameter Estimation and CF Recognition.- Experiment: A Cube-In-Corner Assembly.- Task Planning with Active Sensing.- General Conclusions.

Polyhedral contact formation identification for autonomous compliant motion: exact nonlinear bayesian filtering

This work presents new experimental results for the estimation of large position and orientation inaccuracies of contacting objects during force-controlled compliant motion. The estimation is based on position, velocity, and force measurements. The authors have described the contact modeling and presented some Kalman filter identification results for small inaccuracies. However, when dealing with larger inaccuracies, the nonlinear estimation problem remained unsolved. This problem has now been solved satisfactorily by applying a new Bayesian estimator. The Bayesian filter is valid for static systems (parameter estimation) with any kind of nonlinear measurement equation, subject to Gaussian measurement uncertainty and for a limited class of dynamic systems. Experimental results of this new filter are given for the estimation of the positions and orientations of contacting objects during the cube-in-corner assembly described in the first reference.

Polyhedral contact formation modeling and identification for autonomous compliant motion

This paper describes the contact formation modeling for the identification of geometrical parameters (positions, orientations, and dimensions) of rigid polyhedral objects during the force-controlled execution of contact formation sequences. The following improvements with respect to the state of the art are made: 1) the modeling effort is reduced considerably; 2) the generation of the measurement equations for the online estimators can be automated more easily; 3) the propagation of the geometrical parameter estimates over sequences of contact formations becomes straightforward; and 4) the measurement equations are valid for large uncertainties on the geometrical parameter estimates.

Task planning with active sensing for autonomous compliant motion

Previous research has shown that the execution of contact tasks under uncertainty benefits from on-line estimation of the geometrical contact parameters, such as positions, orientations and dimensions of the contacting objects. However, the constant translational and rotational velocities commonly used to trigger the contact formation (CF) transitions are often not sufficiently exciting to estimate all geometrical parameters. In this paper, we focus on the calculation of a fine-motion task plan, which improves the observation of inaccurately known geometrical parameters. This is called active sensing. Our approach to active sensing is to optimize the task plan (i) by minimizing an objective function, such as the expected execution time, which is an important criterion in industrial applications, and (ii) by constraining the task plans to plans which observe the geometrical parameter estimates to the required accuracy. Active sensing for compliant motion is a new research area. Hence, this paper primarily aims at formulating the active sensing problem and decoupling it into smaller optimization problems. The main contributions of this paper are (i) the definition of the CF-observable parameter space, which allows us to decouple the active sensing requirement for the task plan into a requirement for the CF sequence and requirements for the active sensing motions in each CF, and (ii) the description of practical (suboptimal) solutions and heuristics, making on-line replanning feasible.

A Comparison of Decision Making Criteria and Optimization Methods for Active Robotic Sensing

This work presents a comparison of decision making criteria and optimization methods for active sensing in robotics. Active sensing incorporates the following aspects: (i) where to position sensors, and (ii) how to make decisions for next actions, in order to maximize information gain and minimize costs. We concentrate on the second aspect: Where should the robot move at the next time step?. Pros and cons of the most often used statistical decision making strategies are discussed. Simulation results from a new multisine approach for active sensing of a nonholonomic mobile robot are given.

A demonstration tool with Kalman filter data processing for robot programming by human demonstration

This paper presents a modular demonstration tool for robot programming by human demonstration and an approach for the calibration of the tools sensors. The tool is equipped with a wrench sensor, twelve LED markers for fast and accurate six dimensional position tracking with the Krypton K600 camera system, a compact camera and a laser distance sensor. A gripper mechanism is mounted on the tool for grasping and manipulating objects. The design of the tool specifically focused on the demonstration of compliant motion task, with applications in manipulation and assembly tasks. The calibration approach first uses an extended Kalman Filter to convert the measured positions of three to twelve visible LEDs into the pose of the tool frame relative to the Krypton camera frame. Then, using a non minimal state Kalman filter, the force sensor calibration parameters are calculated, and the orientation of the Krypton camera frame relative to the world frame is defined. This calibration approach is verified in a real world experiment.