Chao Chen

Kui Yang, Xianlei Long, Haoxuan Li et al.

Mobile manipulation is a fundamental capability in embodied intelligence robotics. The growing demand for robust and generalizable manipulation in unstructured household environments has driven rapid progress in embodied intelligence platforms. However, achieving a seamless transfer across the real-to-sim-to-real cycle faces three key challenges, including costly high-fidelity simulation scenes reconstruction, the complexity of systematic strategy evaluation in simulation, and incompatible real-world deployments. To address these challenges, we develop BestMan, a scalable and seamless real-to-sim-to-real platform that bridges the gap between the simulation and the real world, enabling effective strategy development, integration, and deployment for household mobile manipulation. Specifically, we design a novel Automated Scene Generation (ASG) module to reconstruct realistic simulations from real observations. Then, we propose a simulation-guided task formalization and skill learning architecture that supports the flexible integration and large-scale evaluations of hybrid skill strategies in simulation. Finally, to enhance the real-world scalability, we develop a Hardware-agnostic and Unified Middleware (HUM) to ensure seamless and compatible sim-to-real transfer across heterogeneous mobile manipulators for real deployments. Experimental results demonstrate the superior performance of our proposed platform in establishing standardized benchmarks and facilitating promising research in the field of mobile manipulation.

James E. Garrison, Chao Chen, Ilse C. F. Ipsen

Cholesky-QR is among the fastest algorithms for computing the thin QR factorization of tall-and-skinny matrices on GPUs, relying entirely on BLAS-3 operations. However, it is numerically unstable: forming the Gram matrix squares the condition number, causing breakdown when $κ_2(\boldsymbol{A}) \gtrsim 10^8$. We present MRCQR (Mixed-Precision Randomized Cholesky-QR), a stable GPU algorithm that addresses this limitation. MRCQR uses a subsampled randomized trigonometric transform to construct a preconditioner $\boldsymbol{R}_s$ that reduces $κ_2(\boldsymbol{A}\boldsymbol{R}_s^{-1})$ to near unity with high probability, then applies Cholesky-QR in double precision to the preconditioned matrix. The key insight -- supported by perturbation analysis -- is that the preconditioner requires far less accuracy than the final result: single (FP32) precision suffices when $κ_2(\boldsymbol{A}) \lesssim 10^8$, and half (FP16) when $κ_2(\boldsymbol{A}) \lesssim 10^4$. MRCQR produces an explicit orthogonal factor $\widehat{\boldsymbol{Q}}$ satisfying $\|\boldsymbol{I} - \widehat{\boldsymbol{Q}}^\top\widehat{\boldsymbol{Q}}\|_2 = \cal O(\mathbf{u})$ ($\mathbf{u} \approx 10^{-16}$, double-precision unit roundoff) for condition numbers up to $10^{16}$, far beyond the $10^8$ limit of CholQR2. Experiments on an NVIDIA H100 GPU show that MRCQR (FP16) outperforms rand-cholQR by $1.4$--$1.8\times$ across all tested column counts and is $1.8$--$13.5\times$ faster than cuSOLVER geqrf, while the FP16 sketch (used when $κ_2(\boldsymbol{A}) \lesssim 10^4$) is $2\times$ cheaper than FP64 at no accuracy cost.