Optimal Trajectories for The Control of A Truck-Type Mobile Robot Navigating A Roundabout
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Keywords:
Circular Obstacle; Energy Optimization; Mobile Robot; Optimal Control Theory; Pontryagin’s Maximum Principle; Trajectory PlanningAbstract
This study investigates the optimal control of an autonomous truck-type system navigating circular obstacles, considering two performance criteria: minimizing travel time and minimizing energy consumption (control effort). The theoretical analysis employs the Pontryagin Maximum Principle (PMP), which provides necessary conditions for optimality by characterizing switching functions. Based on these conditions, optimal trajectories and corresponding control laws are derived.
Three case studies are presented: Time-Optimal Control of a Truck in the Absence of Circular Obstacles (TOCTACO), Time-Optimal Control of a Truck in the Presence of a Circular Obstacle (TOCTPCO), and Energy-Efficient Truck Path Planning in the Presence of Circular Obstacles (EETPPPCO). The obstacle-free case demonstrates that time-optimal controls follow a typical bang-bang structure. Introducing a circular obstacle modifies the control structure while preserving, under certain conditions, the bang-bang behavior for time minimization. For the energy-optimization scenario, PMP analysis shows that optimal controls may include singular arcs, whose presence and duration influence the trajectory smoothness, maneuver duration, and total energy consumption.
Numerical simulations, performed using a direct trapezoidal collocation method, model the obstacle as a roundabout, a traffic feature commonly encountered by trucks. The results confirm the theoretical predictions and demonstrate that the presence of singular arcs can reduce energy consumption compared to purely bang-bang strategies, even when the maneuver duration increases. The simulations also highlight the sensitivity of optimal trajectories to entry and exit configurations around the roundabout. These findings provide practical insights into the influence of environmental constraints on trajectory planning and support the development of energy-efficient and safe navigation strategies for autonomous truck systems. Future work will focus on designing an autonomous roundabout management strategy that accounts for truck dimensions and operational constraints.
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