Safe and Smooth: Certified Continuous-Time Range-Only Localization

Continuous-Time Range-Only Pose Estimation

“…In contrast to previous work [15], which focuses on position only and provides an optimality certificate for solutions from a local solver, our focus is to formulate tractable SDPs for pose estimation that can be solved quickly for online applications. Additionally, unlike previous methods [3], [16], our method does not require additional odometry sensors; it can be used to generate initial poses without any motion, which we refer to as static initialization.…”

“…As mentioned previously, limitations of such sensor-fusion methods include the need for sufficient motion for full-state observability [7], [8] and the need for additional sensing modalities. More recently, approaches based on Gaussian-process regression [17] have been applied to continuous-time RO position [15] and pose [9] estimation. The benefit of these approaches is that no other sensing modalities are needed as the pose is observable (with multiple tags) under static conditions and with trajectories that lack diverse motion.…”

“…The application of duality theory to generate a certificate of optimality for RO localization was recently described in [15]. Subsequently, an approach to certifiably correct range-aided SLAM with pose variables was demonstrated in [16].…”

“…Subsequently, an approach to certifiably correct range-aided SLAM with pose variables was demonstrated in [16]. Unlike previous works, which focus on certifying batch solutions [15] or requiring additional sensing modalities [3], [10], [16], we focus on computationally tractable SDP relaxations to obtain optimal initial pose and trajectories over a short time horizon using multiple tags on the robot.…”

“…The matrix K is such that p = Kp. Similar to [10], [15], we consider a squared-distance measurement model:…”