## 2 Related Works  
The Next-Best-View (NBV) problem has evolved into a rich family of techniques that balance information gain, motion cost and real-time feasibility across mobile and fixed-base platforms. In the context of Industry 4.0 work-cells--where fixtures, workpieces and even human co-workers may change between shifts--the demand has shifted from object-centric scanning to workspace-centric exploration able to cope with incomplete or outdated CAD data. The paragraphs below review this progression and position our potential-field, collision-based planner with respect to current state-of-the-art techniques. Early NBV research focused on volumetric information gain computed by ray-casting or frontier enumeration. Classical frontier-RRT planners for mobile robots [4] already demonstrated good coverage but struggled with the exponential growth of candidate evaluations in cluttered 3-D scenes. Subsequent benchmarks, such as [PERSON] et al. [5], quantified how various visibility-likelihood models affect reconstruction accuracy, paving the way for more selective candidate generation. Recent \"optimal frontier\" extensions  
Figure 1: Illustration of the NBV problem. reduce this computational burden by evaluating only dynamically-maintained frontier sets; [PERSON] et al. 's sparse RRG approach, for example, halves gain-evaluation time while preserving coverage accuracy [6]. Information-theoretic formulations remain dominant for manipulators dedicated to high-resolution object modeling. Two-stage planners [7] that first choose coarse viewpoints and then refine them locally or that adapt voxel size through multi-resolution max-flow optimization [8] offer excellent surface completeness, yet they still rely on millions of rays per NBV cycle. When occlusions are severe, shadow-casting NBV [9] provides a GPU-friendly alternative, but at the expense of extra memory for visibility maps. Our method departs from this family by replacing ray-casting with a fast collision-set test on the live octomap. Utility-balanced planners explicitly mix exploration reward with kinematic or energetic costs. Environment-guided exploration [10] augments frontier gain with time-and-effort penalties and [PERSON] et al. optimize frontier costs in real time using local map statistics [11]. We adopt the same philosophy but cast distance, rotation change, and collision-derived gain into a single scalar fitness; the ablation study in Section 4 shows that the unequal weighting of these terms yields shorter paths than the uniform weighting traditionally assumed in utility literature. Learning-based NBV has gained momentum because neural policies can amortize the cost of ray-casting across training episodes. BENBV-Net learns a boundary-exploration policy that generalizes across objects [12], [PERSON] & [PERSON] predict gain maps with a lightweight CNN so that only the most promising voxels are evaluated online [13], and [PERSON] et al. train a deep-RL agent that maximizes fruit visibility in agricultural orchards [14]. While these approaches excel once training data exist, their reliance on object or environment priors limits applicability in brown-field factories where layouts change daily. Our training-free strategy therefore complements learning-based NBV by offering a drop-in solution for cells that are re-configured on the fly. Industry-oriented surveys emphasize that up-to-date environment models are essential for collision-free motion planning, scheduling and, digital-twin synchronization [1], the recent synthesis of active mapping and robot exploration trends reaches the same conclusion [15]. Yet most NBV studies still assume static or slowly changing scenes. By computing information gain from current collision geometry rather than pre-existing CAD, our planner inherently handles movable tooling and work-pieces--an aspect under-served in frontier or learning-based work that bakes static occupancy into the reward. Finally, papers that blur the boundary between manipulation and mobility deserve mention.