SDF-Theta*: A Safety- and Smoothness-Aware Global Path Planning Framework for Orchard Robots in Unstructured Environments

Global path planning for autonomous orchard robots must balance obstacle clearance, path smoothness, and trajectory trackability. This balance is difficult to achieve in unstructured orchards, where irregular tree rows, scattered trunks and ground obstacles, and narrow inter-row passages can cause conventional planners to generate low-clearance paths with frequent local turns. This study proposes SDF-Theta*, a safety- and smoothness-aware global path planning framework for orchard robots in unstructured environments. The framework constructs a Euclidean signed distance field (ESDF) from a two-dimensional occupancy planning map and defines a safe navigable domain using the robot width and a grid-discretization approximation margin. Within this domain, the bidirectional SDF-Theta* search performs candidate-node screening, applies Safe LOS checks along candidate connection segments, and uses safety–geometry multi-criteria state selection based on minimum clearance, mean clearance, path length, and turning cost. The resulting initial discrete path is processed through path skeleton refinement and local Bézier curve smoothing. Differential-flatness-based time parameterization then converts the smoothed geometric path into a time-indexed motion reference. In the Orchard Field Experiment, SDF-Theta* increased the minimum obstacle clearance by 16.6% compared with Theta* (ESDF) and achieved a safe path ratio of 100.00%. It also reduced the 99th-percentile curvature, maximum curvature, and total curvature variation by 54.3%, 85.5%, and 82.1%, respectively. Trajectory Tracking Validation yielded a path-overlap ratio of 94.65% at a nearest-path distance threshold of 0.03 m, with no physical collision or map-boundary violation. These results show that SDF-Theta* improved path safety and geometric smoothness and demonstrated trajectory trackability under the tested orchard conditions.