Secure Angle-Based Geometric Elimination (SAGE) for Microrobot Path Planning

Microrobot navigation in constrained environments requires path planning methods that ensure both efficiency and collision avoidance. Conventional approaches, which typically combine graph-based path finding with geometric path simplification, effectively reduce path complexity but often generate collision-prone paths because wall boundaries are not considered during simplification. Therefore, to overcome this limitation, we present Secure Angle-based Geometric Elimination (SAGE), a single-pass path-simplification algorithm that converts pixel-level shortest paths into low-complexity trajectories suitable for real-time collision-free navigation of microrobots. SAGE inspects consecutive triplets (p_i, p_i+1, p_i+2) and removes the middle point when the turning angle is smaller than threshold (∠p_ip_i+1p_i+2 ≤ θ_th) or the direct segment (p_i → p_i+2) is collision-free. Quantitative analysis shows that SAGE achieves approximately 5% shorter path length, 20% lower turning cost and 0% collision rate, while maintaining computation comparable to the Ramer-Douglas-Peucker algorithm. Integration with Dijkstra and RRT planners confirms scalability across complex maze and vascular environments. Experimental microrobot demonstrations show navigation with complete collision avoidance, establishing SAGE as an efficient and reliable framework for high-speed microrobot navigation and automation in lab-on-a-chip, chemical-reaction and molecular-diagnostic systems.