Xun S. Zhou

Multi-robot SLAM with Unknown Initial Correspondence: The Robot Rendezvous Case

This paper presents a new approach to the multi-robot map-alignment problem that enables teams of robots to build joint maps without initial knowledge of their relative poses. The key contribution of this work is an optimal algorithm for merging (not necessarily overlapping) maps that are created by different robots independently. Relative pose measurements between pairs of robots are processed to compute the coordinate transformation between any two maps. Noise in the robot-to-robot observations, propagated through the map-alignment process, increases the error in the position estimates of the transformed landmarks, and reduces the overall accuracy of the merged map. When there is overlap between the two maps, landmarks that appear twice provide additional information, in the form of constraints, which increases the alignment accuracy. Landmark duplicates are identified through a fast nearest-neighbor matching algorithm. In order to reduce the computational complexity of this search process, a kd-tree is used to represent the landmarks in the original map. The criterion employed for matching any two landmarks is the Mahalanobis distance. As a means of validation, we present experimental results obtained from two robots mapping an area of 4,800 m2

Robot-to-Robot Relative Pose Estimation From Range Measurements

In this paper, we address the problem of determining the 2-D relative pose of pairs of communicating robots from (1) robot-to-robot distance measurements and (2) displacement estimates expressed in each robots reference frame. Specifically, we prove that for nonsingular configurations, the minimum number of distance measurements required for determining all six possible solutions for the 3 degree-of-freedom (3-DOF) robot-to-robot transformation is 3. Additionally, we show that given four distance measurements, the maximum number of solutions is 4, while five distance measurements are sufficient for uniquely determining the robot-to-robot transformation. Furthermore, we present an efficient algorithm for computing the unique solution in closed form and describe an iterative least-squares process for improving its accuracy. Finally, we derive necessary and sufficient observability conditions based on Lie derivatives and evaluate the performance of the proposed estimation algorithms both in simulation and via experiments.

Two Efficient Solutions for Visual Odometry Using Directional Correspondence

This paper presents two new, efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm, using a vanishing point for the reference direction, or to make use of an inertial measurement unit commonly available on robots and mobile devices where the gravity vector becomes the reference direction. We provide a simple, closed-form solution and a solution based on algebraic geometry which offers numerical advantages. In addition, we introduce a new method for computing visual odometry with RANSAC and four point correspondences per hypothesis. In a set of real experiments, we demonstrate the power of our approach by comparing it to the five-point method in a hypothesize-and-test visual odometry setting.

Interrobot Transformations in 3-D

In this paper, we provide a study of motion-induced 3-D extrinsic calibration based on robot-to-robot sensor measurements. In particular, we introduce algebraic methods to compute the relative translation and rotation between two robots using known robot motion and robot-to-robot (1) distance and bearing, (2) bearing-only, and (3) distance-only measurements. We further conduct a nonlinear observability analysis and provide sufficient conditions for the 3-D relative position and orientation (pose) to become locally weakly observable. Finally, we present a nonlinear weighted least-squares estimator to refine the algebraic pose estimate in the presence of noise. We use simulations to evaluate the performance of our methods in terms of accuracy and robustness.

3D relative pose estimation from six distances

In this paper, we present three fast, hybrid numericalgebraic methods to solve polynomial systems in floating point representation, based on the eigendecomposition of a so-called multiplication matrix. In particular, these methods run using standard double precision, use only linear algebra packages, and are easy to implement. We provide the proof that these methods do indeed produce valid multiplication matrices, and show their relationship. As a specific application, we use our algorithms to compute the 3D relative translation and orientation between two robots, based on known egomotion and six robotto-robot distance measurements. Equivalently, the same system of equations arises when solving the forward kinematics of the general Stewart-Gough mechanism. Our methods can find all 40 solutions, trading off speed (0.08s to 1.5s, depending on the choice of method) for accuracy.

Determining 3-D Relative Transformations for Any Combination of Range and Bearing Measurements

In this paper, we address the problem of motion-induced 3-D robot-to-robot extrinsic calibration that is based on ego-motion estimates and combinations of interrobot measurements (i.e., distance and/or bearing observations from either or both of the two robots, recorded across multiple time steps). In particular, we focus on solving minimal problems, where the unknown 6-degree-of-freedom (DOF) transformation between the two robots is determined based on the minimum number of measurements necessary to find a finite set of solutions. In order to address the very large number of possible combinations of interrobot observations, we identify symmetries in the measurement sequence and use them to prove that any extrinsic robot-to-robot calibration problem can be solved based on the solutions of only 14 (base) minimal problems. Moreover, we provide algebraic (closed-form) and efficient symbolic-numerical (analytical) solution methods to these minimal problems. Finally, we evaluate the performance of our proposed solvers through extensive simulations and experiments.

Determining the robot-to-robot 3D relative pose using combinations of range and bearing measurements (Part II)

In this paper, we address the problem of motion-induced 3D robot-to-robot extrinsic calibration based on different combinations of inter-robot measurements (i.e., distance and/or bearing observations) and ego-motion estimates, recorded across multiple time steps. In particular, we focus on solving minimal problems where the unknown 6-degree-of-freedom transformation between two robots is determined based on the minimum number of measurements necessary for finding a discrete set of solutions. In our previous work [1], we have shown that only 14 base systems need to be solved, and provided closed-form solutions for three of them. This paper considers the remaining systems and provides closed-form solutions to most of them, while for some of the most challenging problems, we introduce efficient symbolic-numerical solution methods. Finally, we evaluate the performance of our proposed solvers through extensive simulations.

Determining the robot-to-robot 3D relative pose using combinations of range and bearing measurements: 14 minimal problems and closed-form solutions to three of them

In this paper, we address the problem of motioninduced 3D extrinsic calibration based on different combinations of inter-robot measurements (i.e., distance and/or bearing observations from either or both of the two robots, recorded across multiple time steps) and ego-motion estimates. In particular, we focus on solving minimal problems where the unknown 6-degree-of-freedom transformation between the two robots is determined based on the minimum number of measurements necessary for finding a discrete set of, in general, multiple solutions. In order to address the very large number of possible combinations of inter-robot observations, we identify symmetries in these problems and use them to prove that any of the possible extrinsic robot-to-robot calibration problems can be solved based on the solution of only 14 (base) minimal problems. Finally, we derive analytical solutions to three of these base problems, and evaluate their performance through extensive simulations.

Optimized motion strategies for localization in leader-follower formations

This paper addresses the problem of determining the optimal robot trajectory for localizing a robot follower in a leader-follower formation using robot-to-robot distance or bearing measurements. In particular, maintaining a perfect formation has been shown to reduce the localization accuracy (as compared to moving randomly), or even leads to loss of observability when only distance or bearing measurements are available and the robots move on parallel straight lines. To address this limitation, we allow the follower to slightly deviate from its desired formation-imposed position and seek to find the next best location where it should move to in order to minimize the uncertainty about its relative, with respect to the leader, position and orientation estimates. We formulate and solve this non-convex optimization problem analytically and show, through extensive simulations, that the proposed optimized motion strategy leads to significant localization accuracy improvement as compared to competing approaches.