Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

Abstract

In this paper, mobile robot navigation on a 3D terrain with a single obstacle is addressed. The terrain is modelled as a smooth, complete manifold with well-defined tangent planes and the hazardous region is modelled as an enclosing circle with a hazard grade tuned radius representing the obstacle projected onto the terrain to allow efficient path-obstacle intersection checking. To resolve the intersections along the initial geodesic, by resorting to the geodesic ideas from differential geometry on surfaces and manifolds, we present a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. The replanning algorithm generates two new paths, each a composition of two geodesics, connected via critical points whose locations are found to be heavily relying on the exploration of the terrain via directional scanning on the tangent plane at the first intersection point of the initial geodesic with the circle. An advantage of this geodesic path replanning procedure is that traversability of terrain on which the detour path traverses could be explored based on the local Gauss-Bonnet Theorem of the geodesic triangle at the planning stage. A simulation demonstrates the practicality of the analytical geodesic replanning procedure for navigating a constant speed point robot on a 3D hill-like terrain.

Hybrid A*-Based Valley Path Planning Algorithm for Aircraft

“…If q n is already in the closed list S closed , continue (lines 13-15); if q n is already in the open list S open , check whether the cost of new q n is larger than that of original q n . If this is the case, replace original q n with new q n (lines [16][17][18][19][20]. Upon completion of the entire search process, a feasible path γ can be derived by tracing back from q goal to q start and obtaining valley path γ (line 23).…”

“…However, the paper might not thoroughly address dynamic energy constraints, such as varying energy consumption rates based on terrain types, or unexpected environmental factors, which are crucial for realistic energy-efficient path planning. Wu et al [20] presented a geodesic-based planning and replanning algorithm as a new method for obstacle avoidance on a 3D terrain without using boundary following on the obstacle surface. A simulation demonstrated the practicality of the analytical geodesic replanning procedure for navigating a constant-speed-point robot on a 3D hill-like terrain.…”

A comprehensive analysis for classification and regression of surface points based on geodesics and machine learning algorithms

“…Parameterization of Bezier curves is used for optimization to determine the smooth path that satisfies the constraints of the robot. In (Wu et al ., 2016), a method for navigating a mobile robot using geodesics is described. To numerically compute high-order derivatives of geodesic curves on surfaces, Scholz and Maekawa used a new approach in (Scholz and Maekawa, 2021).…”