Imu preintegration gtsam. Structure from Motion.

Imu preintegration gtsam next. The pose estimation is done in IMU frame and IMU messages are always required as one of the input. Contribute to haidai/gtsam development by creating an account on GitHub. I am uing the ros_imu_bno055 package to take the data via USB, i feel it has a lot of noise, resulting into this Aug 27, 2018 · 中文文档：IMU预积分总结与公式推导. Structure from Motion 5. NOTE: NonlinearEquality forces the optimizer to use QR rather than Cholesky QR is much slower than Cholesky, but numerically more stable. May 18, 2019 · Christian Forster, Luca Carlone, Frank Dellaert, and Davide Scaramuzza, “IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation”, Robotics: Science and Systems (RSS), 2015. g. Mar 8, 2020 · preintegration formulas when IMU are either noise free, or bias free. 55 * Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation, Saved searches Use saved searches to filter your results more quickly Sep 7, 2021 · Inertial measurement unit (IMU) preintegration is widely used in factor graph optimization (FGO); e. Todd Lupton and Salah Sukkarieh, "Visual-Inertial-Aided Navigation for High-Dynamic Motion in Built Environments Without Initial Conditions", TRO, 28(1):61-76, 2012. We demonstrate that the preintegration approach can be viewed as Lidar IMU localization system based on NDT matching - mysterybc/ndt_imu_localization [IROS 2023] Fast LiDAR-Inertial Odometry via Incremental Plane Pre-Fitting and Skeleton Tracking - xingyuuchen/LIO-PPF Main functionality: void update (const Vector3 &measuredAcc, const Vector3 &measuredOmega, const double dt, Matrix9 *A, Matrix93 *B, Matrix93 *C) override: Update preintegrated measurements and get derivatives It takes measured quantities in the j frame Modifies preintegrated quantities in place after correcting for bias and possibly sensor pose NOTE(frank): implementation is different in two imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization GTSAM includes a state of the art IMU handling scheme based on. Email: fforster,sdavideg@ifi. imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization graph_. We constrain the first pose such that it cannot change from its original value during optimization. Bias update with Lie exponential coordinates; Proposed rotating Earth and Coriolis effect preintegration; Debug of the original rotating Earth and Coriolis effect preintegration Jul 26, 2021 · So I tried to reinstall GTSAM 4. 6-axis IMU works now. An e-book based on a set of executable python notebooks to illustrate GTSAM. To verify the IMU preintegration in Symforce we test it on the well-known KITTI dataset and closely replicate the IMU preintegration example from GTSAM. IMU_Preintegration - second pass at MATLAB implementation of IMU factors and solvers. To start, I focused on building a working setup using only the IMU and wheel odometry. Kalman Smoother Inertial Estimation with Imu Preintegration. The estimated state is a 15-dimensional vector as shown in (1). ch ySchool of Interactive Computing, Georgia Institute of Technology, Atlanta LVI-SAM: Tightly-coupled Lidar-Visual-Inertial Odometry via Smoothing and Mapping - TixiaoShan/LVI-SAM Sep 18, 2019 · The robot’s inertial measurements can be incorporated into the graph using the preintegrated IMU factor built into GTSAM 4. This object requires various parameters such as the sensor covariances, an initial estimate of the bias, and a potential tranform bodyPsensor is the IMU is not coincidental with the body frame. Navigation state: Pose (rotation, translation) + velocity NOTE(frank): it does not make sense to make GTSAM is a library of C++ classes that implement smoothing and mapping (SAM) in robotics and vision, using factor graphs and Bayes networks as the underlying computing paradigm rather than sparse m Oct 12, 2023 · IMU calibration was not very complicated, as the IMU was rotated by 90 degrees in Y-axis by default and fixing that fixed the orientation. It works a little bit different then the above mentioned approaches in that it estimates Visual Inertial Odometry (VIO) / Simultaneous Localization & Mapping (SLAM) using iSAM2 framework from the GTSAM library. Advanced Kalman Smoothing 1. GTSAM by Example 1. A manifold defines a space in which there is a notion of a linear tangent space that can be centered 中文文档：IMU预积分总结与公式推导. 2 and I noticed that when GTSAM is not installed or when I install GTSAM 4. Final option is to implement the algorithm from VINS Mono. To implement the 6-DOF GNSS/IMU integration method, we used a GNSS/IMU integration algorithm based on the IMU preintegration factor using GTSAM [28, 29]. In this article, we revisit the preintegration theory and propose a novel interpretation to understand it from a nonlinear observer perspective, specifically the parameter estimation-based observer (PEBO). imuIntegratorOpt_ =new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization void resetOptimization() { // gtsam相关优化参数重置 imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization Jul 9, 2023 · The inertial measurement unit (IMU) preintegration approach nowadays is widely used in various robotic applications. Given the estimate of the bias, return a NavState tangent vector summarizing the preintegrated IMU measurements so far NOTE(frank): implementation is different in two versions. 5. To switch to the RSS 2015 version, set the flag GTSAM_TANGENT_PREINTEGRATION to OFF. GTSAM is a library of C++ classes that implement smoothing and mapping (SAM) in robotics and vision, using factor graphs and Bayes networks as the underlying computing paradigm rather than sparse m imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization Inertial Estimation with Imu Preintegration 5. Our GTSAM fork of at this url contains implementation for. ; IMU_Preintegration - second pass at MATLAB implementation of IMU factors and solvers. You signed out in another tab or window. // IMU preintegration parameters. 0 from Ubuntu PPA the Imu-Preintegration issue is resolved. Indelman, and F. 来源于bitbucket的gtsam，用于个人加注释，著作权归原作者所有. cpp generate matches using bundle adjustment details explained in paper Jan 8, 2013 · Add a single IMU measurement to the preintegration. md at develop · borglab/gtsam imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization Welcome to the GTSAM users group. cpp: check out distance of two measurements for the same plane test_vro_imu_graph. cpp: different from test_vro_imu_graph. Fix some extrinsic parameter importing problems. However, when I see s Integration is done incrementally (ideally, one integrates the measurement as soon as it is received from the IMU) so as to avoid costly integration at time of factor construction. The Maximum-a-Posteriori Problem¶. - taroz/gtsam-4. Carlone, Z. GTSAM is a library of C++ classes that implement smoothing and mapping (SAM) in robotics and vision, using factor graphs and Bayes networks as the underlying computing paradigm rather than sparse m imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization Oct 20, 2022 · I see preintegration in IMU-fused SLAM literatures, which mention that preintegration is useful in avoiding to recompute the IMU integration between two consecutive keyframes. accumulates a packet of measurements and adds multiple ones in a single factor (the paper linked above has more details). A video showing an example of the execution. - gtsam/README. This factor relates the base pose, velocity, and IMU biases across consecutive timesteps. A primer on GTSAM Expressions, which support (superfast) automatic differentiation, can be found on the GTSAM wiki on BitBucket. Saved searches Use saved searches to filter your results more quickly GTSAM is a library of C++ classes that implement smoothing and mapping (SAM) in robotics and vision, using factor graphs and Bayes networks as the underlying computing paradigm rather than sparse matrices. I can see the pointclouds in the rviz, global map and local map are appearing for a while from time to time, but they are not complete - they are Test programs to understand how GTSAM's imu preintegration algorithm works. Read about important GTSAM-Concepts here. II. You switched accounts on another tab or window. GTSAM is open source under the BSD license, see the LICENSE and LICENSE. Introduction¶. Dellaert, “Eliminating conditionally independent sets in factor graphs: A unifying perspective based on smart factors,” in Proceedings - IEEE International Conference on Robotics and Automation , 2014. Firstly, we derive a new IMU factor, motivated by the work in with the corresponding preintegration method. 0 optimization. , for legged robot odometry [29,30], differential driv e motion model [31], unknown time offset [32], wheel odometry [33,34], and Aug 1, 2016 · integrated the proposed IMU preintegration in a state-of-the-art VIO pipeline and tested it on real and simulated datasets. 3. 0 optimization toolbox [7]. Key Concepts. boost::shared_ptr<PreintegratedImuMeasurements::Params> imuParams() { // We use the sensor specs to build the noise model for the IMU factor. Inertial Estimation with Imu Preintegration. com ments between selected keyframes. 3a Apr 9, 2022 · gtsam官方文档：The new IMU Factor 本文为gtsam imu预积分文档学习笔记，为gtsam基于切向量实现的imu预积分的理论基础。 导航状态 定义导航状态为 Xbn={Rbn,Pbn,Vbn}X^n_b=\{R^n_b,P^n_b,V^n_b\}Xbn ={Rbn ,Pbn ,Vbn } 上角标n：导航(navigation)坐标系 下角标b：载体(body)坐标系 下文均省略 I passed the symbolic imu_preintegration_update function to Codegen. 5. Jul 28, 2020 · IMU preintegration is adapted, e. function to create a runtime variant, then wrote a very light wrapper class that stores the state and calls the function on each new measurement. 1. Jan 8, 2013 · Given the estimate of the bias, return a NavState tangent vector summarizing the preintegrated IMU measurements so far . We skip GPS measurements such that we have 10 poses with an ImuFactor for every measured pose, but optimize the pose at every time step to retrieve IMU rate estimates. uzh. Our imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization Main functionality: void update (const Vector3 &measuredAcc, const Vector3 &measuredOmega, const double dt, Matrix9 *A, Matrix93 *B, Matrix93 *C) override: Update preintegrated measurements and get derivatives It takes measured quantities in the j frame Modifies preintegrated quantities in place after correcting for bias and possibly sensor pose NOTE(frank): implementation is different in two GTSAM by Example. - masoug/imu-preintegration-experiments imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization Given the estimate of the bias, return a NavState tangent vector summarizing the preintegrated IMU measurements so far NOTE(frank): implementation is different in two versions. e. Public Member Functions inherited from gtsam::PreintegrationBase Optional sensor frame (pose of the IMU in the body frame) Reimplemented from gtsam::PreintegrationBase . This can be modified to also estimate the temporal offset as seen in this paper. However, most existing IMU preintegration models ignore the Earth's rotation and lack delicate integration processes, and these limitations severely degrade the INS 2. ch ySchool of Interactive Computing, Georgia Institute of Technology, Atlanta Sep 18, 2020 · IMU preintegration technology has been widely used in the optimization-based sensor fusion framework, in order to avoid reintegrating the high-frequency IMU measurements at each iteration and maintain the ability of bias correction when bias estimation changes. The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the nonlinear functions around an initial linearization point, then solve the linear system to update the linearization point. Contribute to gisbi-kim/SC-LIO-SAM development by creating an account on GitHub. There are a few details I'd like to work out here before putting up a PR. - PengYu-Team/Co-LRIO Read about important GTSAM-Concepts here. Additionally, either GPS (NavSatFix) or 6DOF pose (PoseWithCovarianceStamped) messages are required to constrain the drift in the IMU preintegration. cpp: Implementation of VIO+Plane SLAM test_ba_imu_graph. Public Member Functions PreintegrationParams (): Default constructor for serialization only. - skyrim835/LVI-SAM-modified Nov 14, 2017 · In this paper, we present a visual-inertial navigation system (VINS) that combines the visual SLAM approach and IMU preintegration technique [33,38] beyond the framework of ORB-SLAM and PTAM . 2 vision factors in the GTSAM 4. GTSAM includes a state of the art IMU handling scheme based on. Jan 25, 2022 · Protected Attributes: Eigen::Matrix< double, 15, 15 > preintMeasCov_ Protected Attributes inherited from gtsam::ManifoldPreintegration: NavState : deltaXij_ Pre-integrated navigation state, from frame i to frame j Note: relative position does not take into account velocity at time i, see deltap+, in [2] Note: velocity is now also in frame i, as opposed to deltaVij in [2]. 5 days ago · Christian Forster, Luca Carlone, Frank Dellaert, and Davide Scaramuzza, “IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation”, Robotics: Science and Systems (RSS), 2015. . GTSAM is a C++ library that implements smoothing and mapping algorithms using factor-graphs. LIO-SAM is publishing in the map topic from time to time. GTSAM includes several nonlinear optimizers to perform this step. Please feel free to ask/answer/discuss any questions and/or topics you might have with regards to GTSAM, the Georgia Tech Smoothing and Mapping toolbox. PreintegrationParams (const Vector3 &n_gravity): The Params constructor insists on getting the navigation frame gravity vector For convenience, two commonly used conventions are provided by named constructors below. Bayesian inference using Factor graphs¶. Factor Graphs and GTSAM: A Hands-on Introduction. . structurless vision factors in the GTSAM 4. Full smoothing problem¶ A ROS2 package of CoLRIO: LiDAR-Ranging-Inertial Centralized State Estimation for Robotic Swarms. We build upon this work and present a preintegration theory that properly addresses the manifold structure of the rotation group SO(3). IMU Preintegration¶. This project is designed for students to learn the front-end and back-end in a Simultaneous Localization and Mapping (SLAM) system. - masoug/imu-preintegration-experiments Dec 21, 2023 · We compared the proposed method with a conventional general 6-DOF GNSS/IMU integration method. double deltaTij_ Time interval from i to j. Protected Attributes inherited from gtsam::PreintegrationBase: boost::shared_ptr< Params > p_ Bias biasHat_ Acceleration and gyro bias used for preintegration. Here’s the approach I took: I accumulate IMU data and integrate it using PreintegratedImuMeasurements until I receive a wheel odometry See full list on github. Gaussian Inference 1. pose_i: Previous pose key : vel_i: Previous velocity key : pose_j: Current pose key : vel_j: Current velocity key : bias_i: Previous bias key : bias_j: Current bias key preintegration theory. virtual boost::shared_ptr< ManifoldPreintegration > clone const Dummy clone for MATLAB. Tutorials¶. 彻底重构了原版 LIO-SAM：工程级实现、Google代码风格，iKd-Tree、预积分、建图、在线动态过滤。 - coolaogege/Faster-LIO-SAM A convenient base class for creating your own NoiseModelFactor with 3 variables. D. This code was used for the comparision against the current state-of-the-art discrete method in GTSAM by Forster et al. This example illustrates how ISAM2 (Incremental Smoothing and Mapping), whose implementation is available with GTSAM, can be used to solve a 2D SLAM problem from noisy range measurements to some landmarks. Our Dec 8, 2015 · Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. This is not convenient, however, a mathematical trick helps us make the between… Jun 24, 2022 · For factor graphs to be more efficient with IMU processing you typically use an algorithm called IMU preintegration. 34 #ifdef GTSAM_TANGENT_PREINTEGRATION. Oct 29, 2024 · I'm setting up a state estimation pipeline for my robot, which is equipped with an IMU, wheel odometry, and a 2D lidar. cpp: Implementation of visual SLAM based on gtsam test_plane_check_vo. Batch Optimization¶. virtual boost::shared_ptr< ManifoldPreintegration > Integration is done incrementally (ideally, one integrates the measurement as soon as it is received from the IMU) so as to avoid costly integration at time of factor construction. The use of preintegrated IMU measure-ments was first proposed in [2] and consists of combining many inertial measurements between two keyframes into a single relative motion constraint. GTSAM is a library of C++ classes that implement smoothing and mapping (SAM) in robotics and vision, using factor graphs and Bayes networks as the underlying computing paradigm rather than sparse matrices. T echnical Report GT-RIM-CP&R-2012-002, Georgia Institute of Tec hnology, GTSAM includes a state of the art IMU handling scheme based on. imu_preint_matlab - initial pass at MATLAB implementation of IMU factors, and a GTSAM solution for an IMU-only factor graph over the Cassie Blue data. Contribute to watsonryan/gtsam development by creating an account on GitHub. graph->add(BetweenFactor<imuBias::ConstantBias>( B(correction_count - 1), B(correction_count), zero_bias, bias_noise_model)); Contribute to robustrobotics/gtsam development by creating an account on GitHub. BSD files. It includes the pose_i: Previous pose key : vel_i: Previous velocity key : pose_j: Current pose key : vel_j: Current velocity key : bias: Previous bias key gtsam_fusion_ros. Since IMU preintegration technology was first proposed, several improved versions have been designed by changing the attitude imu_preint_matlab - initial pass at MATLAB implementation of IMU factors, and a GTSAM solution for an IMU-only factor graph over the Cassie Blue data. Vision data can be incorporated into the graph using a number of different factors depending on the sensor type and application. The preintegration allows us to accurately summarize hundreds of inertial measurements into a single relative motion constraint. Structure from Motion. Contribute to PetWorm/IMU-Preintegration-Propogation-Doc development by creating an account on GitHub. The derivation is based on the continuous preintegration theory. I wanted to know what imu package are you using to get the imu data. See the INSTALL file for more detailed installation instructions. Lidar without ring works now. Jan 8, 2013 · Add a single IMU measurement to the preintegration. Here we will use a trust-region method known as Powell’s Degleg. The objective is that using feature_tracker in VINS-MONO as front-end, and GTSAM as back-end to implement a visual inertial odometry (VIO) algorithm for real-data collected by a vehicle: The MVSEC Dataset. It includes the Read about important GTSAM-Concepts here. You may want to optimize variable types other than GTSAM provided Vector, SE(2), SO(3), SE(3), etc… (although GTSAM provides a lot!) e. If you are using the factor in academic work, please cite the publications above. imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization Here we provide a complete system for visual-inertial navigation using synthetically generated vision and inertial measurements. These factors allow the use of high-rate IMUs in smoothing by summarizing many IMU measurements into one, in a way that still permits efficient and accurate relinearization and estimation of biases, closely following the methods of Lupton and Sukkarieh in TRO 2012. Mar 31, 2024 · You signed in with another tab or window. Following the preintegration scheme proposed in [2], the ImuFactor includes many IMU measurements, which are "summarized" using the PreintegratedIMUMeasurements IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation Christian Forster , Luca Carlone y, Frank Dellaert , and Davide Scaramuzza Robotics and Perception Group, University of Zurich, Switzerland. Data structure gtsam::Values can now take any type, provided the necessary gtsam::traits are defined. toolbox [30]. Scaramuzza, IMU Preintegration on. Bayesian inference using Factor graphs; The Maximum-a-Posteriori Problem 开源激光雷达、IMU紧耦合SLAM方案源码阅读学习记录；LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping - ZW628/LIO-SAM-Learning GTSAM by Example. LVI-SAM for easier using (更简单的使用LVI-SAM的方法). Pointcloud_Registration from loam. add ( gtsam:: ImuFactor (s_prev_ic, s_prev_vel, s_ic, s_vel, s_bias, pre_integr_data)); Note that the implementation in GTSAM has the concept of IMU preintegration, i. 0. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization Oct 26, 2021 · A while ago, I had explored the theory of IMU preintegration in the context of sensor fusion using a factor graph. Kalman Smoother 1. The optimization backend and IMU dynamics/preintegration is based on: L. Contribute to linghusmile/GTSAM development by creating an account on GitHub. The documentation for this class was generated from the following files: PreintegrationBase is the base class for PreintegratedMeasurements (in ImuFactor) and CombinedPreintegratedMeasurements (in CombinedImuFactor). 4. Our first contribution is a preintegration theory that properly addresses the manifold struc-ture of the rotation group and carefully deals with uncertainty propagation. PreintegrationBase is the base class for PreintegratedMeasurements (in ImuFactor) and CombinedPreintegratedMeasurements (in CombinedImuFactor). Has a partially-working implementation that we developed, as well as a GTSAM reference. Contribute to Cc19245/LVI-SAM-Easyused development by creating an account on GitHub. The basic concept is that to use imu measurement as between factors for optimization we need to know the previous state. Test programs to understand how GTSAM's imu preintegration algorithm works. Both accelerometer and gyroscope measurements are taken to be in the sensor frame and conversion to the body frame is handled by body_P_sensor in PreintegrationParams . py: ROS node to run the GTSAM FUSION. , in visual-inertial navigation system and global navigation satellite system/inertial navigation system (GNSS/INS) integration. Reload to refresh your session. Following the preintegration scheme proposed in [2], the ImuFactor includes many IMU measurements, which are "summarized" using the PreintegratedIMUMeasurements Jul 13, 2015 · release our implementation of the IMU preintegration and the. To perform preintegration, GTSAM conveniently provides us with an object called PreintegratedImuMeasurements. All preintegration methods are implemented in the GTSAM optimization framework. imuIntegratorImu_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for IMU message thread // imu 预积分器，用于因子图优化 imuIntegratorOpt_ = new gtsam::PreintegratedImuMeasurements(p, prior_imu_bias); // setting up the IMU integration for optimization test_gt_graph. Implemented in gtsam::TangentPreintegration, and gtsam::ManifoldPreintegration. This reduces the size of the graph and thus LiDAR-inertial SLAM: Scan Context + LIO-SAM. Beall, V. Only the map-optimization issue remains (after playing the rosbag). May 25, 2021 · I am trying to perform the similar configuration on my side by using a velodyne VLP16 along with Bosch BNO055 IMU. This release makes improvements to the IMU summary factors. 2. Contribute to qpc001/Feature_Base_Pointcloud_Registration development by creating an account on GitHub. LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping - sram-v/LIO-SAM-ROS2 IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation Christian Forster , Luca Carlone y, Frank Dellaert , and Davide Scaramuzza Robotics and Perception Group, University of Zurich, Switzerland. Kira, C. - vkopli/gtsam_vio GTSAM 2. 1 is a minor update from 2. State space of a mobile manipulator (mobile base + a 7 DOF arm) is SE(2) x R(7). xbjaa tcyrkol rdpkgf qgod csfs iqgie din ikw dsfg qgjwrvkz