Introduction
Urban service robots, such as last-meter delivery platforms, inspection robots, and indoor–outdoor logistics units, increasingly operate in cluttered environments where safe navigation must be balanced against limited onboard energy. In many deployed systems, path planning still prioritizes geometric shortest paths with collision penalties, which can produce stop–turn–go behaviors that increase battery drain and reduce operational endurance. This work proposes an energy-aware planning formulation for differential-drive robots in static polygonal environments, targeting smart city scenarios where repeated missions and charging constraints make energy a first-class criterion rather than an afterthought.
Methods
The workspace is modeled as a bounded planar set with obstacles represented by closed polygons. The robot footprint is modeled as a disk of radius with an additional safety clearance (c) , enforcing a minimum separation (r+c) from all obstacle boundaries. Candidate routes are parameterized as polylines connecting the start and goal through continuous intermediate waypoints, assembled into the decision vector x e R2m .
Energy is modeled through a physically interpretable proxy consistent with differential-drive motion primitives: the robot rotates in place to align with the next segment and then translates along that segment. The objective combines translational effort, proportional to total route length, and rotational effort, proportional to cumulative heading changes and their concentration, capturing the fact that frequent or abrupt turns increase wheel actuation and dissipative losses.
Feasibility is enforced through exact geometric checks for polygonal obstacles. For each segment, collision and clearance are verified via segment–polygon intersection tests and minimum segment-to-polygon distance calculations, eliminating the false negatives that occur with coarse point sampling. Boundary constraints restrict intermediate waypoints to the admissible workspace, and an optional turning constraint bounds inter-segment heading changes to avoid extreme cornering demands. The optimization is solved using continuous metaheuristics, genetic algorithms and particle swarm optimization, with a feasibility-first constraint handling rule: any feasible solution dominates any infeasible solution, among feasible solutions lower energy dominates, and among infeasible solutions lower constraint violation dominates. This removes dependence on penalty weight tuning.
Results
In simulated urban-like layouts with multiple polygonal obstacles and narrow corridors, the feasibility-first energy formulation consistently produced collision-free routes that favored smoother steering sequences compared to distance-only planning and penalty-weighted feasibility schemes. The energy-aware objective reduced stop–turn–go patterns by discouraging sharp heading discontinuities, while the exact polygon distance evaluation improved reliability by preventing missed collisions between sampled points. Across repeated random initializations, both metaheuristics converged to feasible solutions when feasible corridors existed, with a genetic search showing strong exploration in cluttered maps and particle swarms showing rapid improvement in early iterations. The method also demonstrated stable behavior under changes in obstacle shape and arrangement, since feasibility is enforced by dominance rules rather than fragile penalty scaling.
Conclusion
An energy-aware, feasibility-first route planning method is presented for differential-drive robots navigating static polygonal environments, aligned with smart city service robotics where endurance and safety must be co-optimized. The combination of an interpretable energy proxy, exact polygonal clearance checks, and dominance-based constraint handling yields robust feasible trajectories without ad hoc penalty tuning. Future work will integrate platform-specific calibration of energy coefficients from measured power profiles and extend the formulation to time-parameterized control optimization while maintaining polygonal safety guarantees.
