RichMap: A Reachability Map Balancing Precision, Efficiency, and Flexibility for Rich Robot Manipulation Tasks

Reliable robot perception requires not only predicting scene structure, but also identifying where predictions should be treated as unreliable due to sparse or missing observations. We present ContraMap, a contrastive continuous mapping method that augments kernel-based discriminative maps with an explicit uncertainty class trained using synthetic noise samples. This formulation treats unobserved regions as a contrastive class, enabling joint environment prediction and spatial uncertainty estimation in real time without Bayesian inference. Under a simple mixture-model view, we show that the probability assigned to the uncertainty class is a monotonic function of a distance-aware uncertainty surrogate. Experiments in 2D occupancy mapping, 3D semantic mapping, and tabletop scene reconstruction show that ContraMap preserves mapping quality, produces spatially coherent uncertainty estimates, and is substantially more efficient than Bayesian kernelmap baselines.

Many stages of the robotic lifecycle, from morphology synthesis to operation, rely fundamentally on the reachable workspace. However, current methods for approximating workspaces are slow, imprecise, or tied to a single morphology. We introduce Reachability Across Morphologies (RAM): a morphology-conditioned, implicit neural representation that acts as a fast, differentiable surrogate for pose reachability, generalising to unseen morphologies while inherently accounting for self-collisions. RAM is trained on a large-scale dataset of $3\cdot10^{10}$ samples generated solely from forward kinematics, which we publish alongside the model. Experiments show that RAM reaches 84% balanced accuracy at nanosecond inference, 15 percentage points higher than a generative inverse kinematics baseline that also generalises across morphologies, while running three orders of magnitude faster. This speed carries over to downstream tasks, accelerating morphology and trajectory optimisation by one to two orders of magnitude.

Dense point cloud maps, as a typically used mapping representation, are difficult to deploy on resource-constrained robots because their memory consumption grows rapidly with scene scale. Although compact single-model representations reduce memory cost, their fixed geometric expressiveness is insufficient for structurally diverse environments. Existing multi-model methods improve representational flexibility, yet their feature extraction and model selection are often dominated by local geometry, which can cause overfitting and adhesion between objects. To address these issues, this paper presents M2-SMap, a memory-efficient semantic mapping framework based on hierarchical multi-model representation. First, a hierarchical geometric decomposition partitions RGB-D point clouds into compact Gaussian components. Then, a projection-guided semantic annotation mechanism assigns instance identities to each component. Subsequently, these annotations are incorporated into an object-aware Gaussian fusion strategy. Furthermore, a multi-scale feature extraction strategy separates large planar regions, semantic objects, and complex residual structures, which are respectively represented by bounded planes, object-level superquadrics, and GMM primitives. Experiments on three RGB-D sequences show that M2-SMap runs in real time at no less than 29.37 Hz while achieving the lowest primitive count, with an average reduction of 18.7% over the best baseline. It also reduces the mean per-frame number of measured inter-object adhesion cases from 2.808 to 0, demonstrating efficient and semantically consistent scene representation.