Udo Frese

A multilevel relaxation algorithm for simultaneous localization and mapping

This paper addresses the problem of simultaneous localization and mapping (SLAM) by a mobile robot. An incremental SLAM algorithm is introduced that is derived from multigrid methods used for solving partial differential equations. The approach improves on the performance of previous relaxation methods for robot mapping, because it optimizes the map at multiple levels of resolution. The resulting algorithm has an update time that is linear in the number of estimated features for typical indoor environments, even when closing very large loops, and offers advantages in handling nonlinearities compared with other SLAM algorithms. Experimental comparisons with alternative algorithms using two well-known data sets and mapping results on a real robot are also presented.

A Discussion of Simultaneous Localization and Mapping

This paper aims at a discussion of the structure of the SLAM problem. The analysis is not strictly formal but based both on informal studies and mathematical derivation. The first part highlights the structure of uncertainty of an estimated map with the key result being “Certainty of Relations despite Uncertainty of Positions”. A formal proof for approximate sparsity of so-called information matrices occurring in SLAM is sketched. It supports the above mentioned characterization and provides a foundation for algorithms based on sparse information matrices.Further, issues of nonlinearity and the duality between information and covariance matrices are discussed and related to common methods for solving SLAM.Finally, three requirements concerning map quality, storage space and computation time an ideal SLAM solution should have are proposed. The current state of the art is discussed with respect to these requirements including a formal specification of the term “map quality”.

Hierarchical optimization on manifolds for online 2D and 3D mapping

In this paper, we present a new hierarchical optimization solution to the graph-based simultaneous localization and mapping (SLAM) problem. During online mapping, the approach corrects only the coarse structure of the scene and not the overall map. In this way, only updates for the parts of the map that need to be considered for making data associations are carried out. The hierarchical approach provides accurate non-linear map estimates while being highly efficient. Our error minimization approach exploits the manifold structure of the underlying space. In this way, it avoids singularities in the state space parameterization. The overall approach is accurate, efficient, designed for online operation, overcomes singularities, provides a hierarchical representation, and outperforms a series of state-of-the-art methods.

Cartesian impedance control of redundant robots: recent results with the DLR-light-weight-arms

This paper addresses the problem of impedance control for flexible joint robots based on a singular perturbation approach. Some aspects of the impedance controller, which turned out to be of high practical relevance during applications are then addressed, such as the implementation of nullspace stiffness for redundant manipulators, the avoiding of mass matrix decoupling and the related design of the desired damping matrix. Finally, the proposed methods are validated through measurements on the DLR robot.

Off-the-shelf vision for a robotic ball catcher

We present a system for catching a flying ball with a robot arm using off-the-shelf components (PC based system) for visual tracking. The ball is observed by a large baseline stereo camera, comparing each image to a slowly adapting reference image. We track and predict the target position using an extended Kalman filter, also taking into account the air drag. The calibration is achieved by simply performing a few throws and observing their trajectories, as well as moving the robot to some predefined positions.

Closing a Million-Landmarks Loop

We present an improved version of the treemap SLAM algorithm which uses Cholesky factors for representing Gaussians and a hierarchical tree partitioning algorithm derived from the established Kernighan-Lin heuristic for graph bisection. We demonstrate the algorithms efficiency by mapping a simulated building with 1032271 landmarks. In the end, we close a million-landmarks loop in 21 ms, providing an estimate for ap10000 selected landmarks close to the robot, or in 442 ms for computing a full estimate

Kick it with elasticity: Safety and performance in human-robot soccer

The RoboCup community has one definite goal [H. Kitano, M. Asada, RoboCup humanoid challenge: Thats one small step for a robot, one giant leap for mankind, in: IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, IROS1998, Victoria, pp. 419-424, 1998]: winning against the human world soccer champion team by the year 2050. This implies real tackles and fouls between humans and robots, rising safety concerns for the robots and even more important for the human players. Nowadays, similar questions are discussed in the field of physical human-robot interaction (pHRI), but mainly in the context of industrial and service robotics applications. The first part of our paper is an attempt for a pHRI view on human-robot soccer. We take scenes from real soccer matches and discuss what could have happened if one of the teams consisted of robots instead of humans. The most important result is that elastic joints are needed to reduce the impact during collisions. The second and third part consider conversely, how the robot can handle the impact of kicking the ball and how it can reach the velocity of human-level soccer. Again joint elasticity is the key point. Overall, the paper analyzes a vision far ahead. However, all our conclusions are based on concrete simulations, experiments, derivations, or findings from sports science, forensics, and pHRI.

A Proof for the Approximate Sparsity of SLAM Information Matrices

For the Simultaneous Localization and Mapping problem several efficient algorithms have been proposed that make use of a sparse information matrix representation (e.g. SEIF, TJTF, treemap). Since the exact SLAM information matrix is dense, these algorithm have to approximate it (sparsification). It has been empirically observed that this approximation is adequate because entries in the matrix corresponding to distant landmarks are extremely small. This paper provides a theoretical proof for this observation, specifically showing that the off-diagonal entries corresponding to two landmarks decay exponentially with the distance traveled between observation of first and second landmark.

A Multigrid Approach for Accelerating Relaxation-Based SLAM

This paper addresses the problem of simultaneous localisation and mapping (SLAM) by a mobile robot . An incremental SLAM algorithm is introduced that is derived from so-called multigrid methods used for solving partial differential equations. The approach overcomes the relatively slow convergence of previous relaxation methods because it optimizes the map at multiple levels of resolution. The resulting algorithm has an update time that is linear in the number of mapped features, even when closing very large loops, and offers advantages in handling non-linearities compared to previous approaches. Experimental comparisons with alternative algorithms using two well-known data sets are also presented.

How far is SLAM from a linear least squares problem

Most people believe SLAM is a complex nonlinear estimation/optimization problem. However, recent research shows that some simple iterative methods based on linearization can sometimes provide surprisingly good solutions to SLAM without being trapped into a local minimum. This demonstrates that hidden structure exists in the SLAM problem that is yet to be understood. In this paper, we first analyze how far SLAM is from a convex optimization problem. Then we show that by properly choosing the state vector, SLAM problem can be formulated as a nonlinear least squares problem with many quadratic terms in the objective function, thus it is clearer how far SLAM is from a linear least squares problem. Furthermore, we explain that how the map joining approaches reduce the nonlinearity/nonconvexity of the SLAM problem.