  Simultaneous localization and mapping (SLAM) are crucial for autonomous
robots (e.g., self-driving cars, autonomous drones), 3D mapping systems, and
AR/VR applications. This work proposed a novel LiDAR-inertial-visual fusion
framework termed R$^3$LIVE++ to achieve robust and accurate state estimation
while simultaneously reconstructing the radiance map on the fly. R$^3$LIVE++
consists of a LiDAR-inertial odometry (LIO) and a visual-inertial odometry
(VIO), both running in real-time. The LIO subsystem utilizes the measurements
from a LiDAR for reconstructing the geometric structure (i.e., the positions of
3D points), while the VIO subsystem simultaneously recovers the radiance
information of the geometric structure from the input images. R$^3$LIVE++ is
developed based on R$^3$LIVE and further improves the accuracy in localization
and mapping by accounting for the camera photometric calibration (e.g.,
non-linear response function and lens vignetting) and the online estimation of
camera exposure time. We conduct more extensive experiments on both public and
our private datasets to compare our proposed system against other
state-of-the-art SLAM systems. Quantitative and qualitative results show that
our proposed system has significant improvements over others in both accuracy
and robustness. In addition, to demonstrate the extendability of our work, {we
developed several applications based on our reconstructed radiance maps, such
as high dynamic range (HDR) imaging, virtual environment exploration, and 3D
video gaming.} Lastly, to share our findings and make contributions to the
community, we make our codes, hardware design, and dataset publicly available
on our Github: github.com/hku-mars/r3live
