Robot-to-Robot Relative Pose Estimation based on Semidefinite Relaxation Optimization

3-D Inter-Robot Relative Localization via Semidefinite Optimization

“…As an alternative, formulating the relative localization problem as a QCQP problem and using SDP relaxation to deal with non-convexity is proven to be a promising solution [13], which only takes around 0.4 s using the CVX toolbox in Matlab. This idea is quite similar to our previous paper [7], which solves a 2-D relative localization problem using odometry and UWB.…”

“…However, due to that the 3-D SD-WLS optimization problem is highly nonlinear, existing approaches are not computationally efficient [11]. In our previous work [7], the 2-D SD-WLS optimization problem is reformulated as a non-convex QCQP problem and addressed using an SDP strategy. In the next section, we propose to demonstrate that the 3-D SD-WLS can be addressed using a similar method.…”

“…, N are noise free or corrupted by small noise, 2 the global optimum of the original QCQP can be found by optimizing its SDP relaxation, which means that f * Opt = f * SDP . Proof: See Appendix B in [7].…”

“…A Visual-Inertial-UWB solution, which addresses the 3-D relative localization problem in an unmanned aerial vehicle collaboration application, is proposed in [6]. In our previous work [7] and some other related work [8], [9], the odometric (IMU and/or wheel encoder) information and UWB ranging measurements are combined to determine the relative pose between robots. Essentially, the above literature addresses the relative localization by combining odometric information and inter-robot measurements like bearing, distance, position, or some combination of them.…”

Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search

“…Even though noise and outliers are ubiquitous in geometric vision, and non-convex formulations and their semidefinite relaxations have been widely used in a large body of papers [34,2,25,19,42,16,15,35,8,9,10,48,28,1,38,63,26,27,3,50], much fewer works [17,43,24,49,31,57,62,53,39] 2 provide theoretical insights on the robustness of semidefinite relaxations to noise, only a few semidefinite relaxations [14,36,59,60] are empirically robust to outliers, and only one paper [56] on rotation synchronization gives theoretical guarantees for noise, outliers, and both. Complementary to the story of [52] and inheriting the spirit of [56], in this paper we question whether "a specific semidefinite relaxation" for "robust rotation search" is "tight" or not, and provide tightness characterizations that account for the presence of noise, outliers, and both.…”