Compressed Orientation Reachability Maps for Sub-Second Robotic Needle Entry Point Planning

Mobile manipulator robots rarely reposition their base during manipulation, because doing so requires real-time knowledge of how well the arm can reach its surroundings among obstacles. Reachability maps (RMs) encode this knowledge, but existing methods are slow, coarse (typically 5 cm), or ignore real obstacles. This article asks whether a neural network can predict an obstacle-aware RM at 2 cm resolution from a live depth camera, on embedded hardware, fast enough for online use. We present HERON, a 3D U-Net trained on RMs computed with the GPU-accelerated inverse kinematics of cuRobo, first on synthetic scenes and then on real depth data, and deployed on a Jetson AGX Orin with TensorRT and INT8 quantization. HERON predicts the RM of a 2.56 m cube around the arm in 115 ms on average, for a measured system rate of 8.57 Hz, close to the 10 Hz update rate of the obstacle map, whereas computing the same map with cuRobo takes about 90 min. Against the cuRobo ground truth, 95% of the voxels lie within 1 class out of 51 with the FP32 model and within 3 classes with the INT8 model, with a Pearson correlation of 0.99 and a quadratic weighted kappa above 0.9. Accuracy degrades mainly at the workspace boundaries.

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.

We propose a workspace-fibered decomposition framework for motion planning in nR planar redundant manipulators operating in cluttered environments. Rather than planning directly in the full n-dimensional configuration space, the method incrementally constructs obstacle-constrained reachable workspaces of lower-dimensional non-redundant sub-chains and recursively lifts them through redundant orientation fibers. This yields a sequence of reduced planning manifolds that preserve branch-consistent reachability structure while avoiding explicit construction of the full configuration-space obstacle geometry. We first establish that, for planar position-only manipulators, the obstacle-constrained reachable workspace induced by the minimal non-redundant sub-chain provides an exact characterization of feasibility with respect to the connected component of the start configuration, enabling early infeasibility detection prior to introducing redundant degrees of freedom (DOF). We then introduce an incremental fiber-lifting procedure that propagates reachable workspace structure through successive redundant links while enforcing local inverse-kinematic branch consistency using Jacobian determinant continuity constraints. The resulting representation admits efficient reduced-space planning directly on recursively-constructed workspace-fiber manifolds. Experimental results on redundant nR planar manipulators demonstrate that the proposed construction preserves collision-free connectivity structure across successive lifting stages while substantially reducing collision checking complexity relative to direct configuration space reasoning.