Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots

Keywords: Car-like robot Trajectory planning Time-optimal control Simultaneous dynamic optimization Interior-point method Computational guidance and control a b s t r a c t Trajectory planning in robotics refers to the process of finding a motion law that enables a robot to reach its terminal configuration, with some predefined requirements considered at the same time. This study focuses on planning the time-optimal trajectories for car-like robots. We formulate a dynamic optimization problem, where the kinematic principles are accurately described through differential equations and the constraints are strictly expressed using algebraic inequalities. The formulated dynamic optimization problem is then solved by an interior-point-method-based simultaneous approach. Compared with the prevailing methods in the field of trajectory planning, our proposed method can handle various user-specified requirements and different optimization objectives in a unified manner. Simulation results indicate that our proposal efficiently deals with different kinds of physical constraints, terminal conditions and collision-avoidance requirements that are imposed on the trajectory planning mission. Moreover, we utilize a Hamiltonian-based optimality index to evaluate how close an obtained solution is to being optimal. Robotic trajectory planning refers to the process of finding a motion law to enable a robot to move from its initial configuration to a desired terminal configuration by simultaneously considering some predefined requirements [1]. Trajectory planning has become a critical aspect of automation science; the applications of this process range from satellite orbit transfer [2], missile guidance [3], unmanned aerial vehicle navigation [4–6], anti-submarine search [7,8], hazardous environment exploration [9] and autonomous parking assistance [10,11]. In this work, we focus on the trajectory planning of car-like robots. A car-like robotic model can represent a wide range of vehicles with steering wheels and power motors [12], which may be the reason why such robots have been widely studied in the past two decades [13,14]. Although some relevant commercial productions are available, they can still be improved substantially regarding smartness and autonomy. In fact, many key parts of real-world deployment phases are ad hoc and manual [15]. Ref. [16] even pointed out that there had been few artificial systems that could outperform an experienced human driver (who also can be regarded as a system, although imperfect, yet the best one known). Therefore, further investigations are necessary to develop smart decision-making capability in robots. Typically a car-like robot is a nonholonomic system [17]. A system is said to be holonomic if all the system constraints can be …