Interest in wheeled mobile robots (WMRs) is growing rapidly due to much broad range of their potential applications - industrial automation, undersea/planet exploration, nuclear/explosives handling, warehousing, security, agricultural machinery, military, education, mobility for the disabled, and personal robots, etc.
Most researches considering dynamic model of WMRs confined to dynamic constraints of input torques only or just limitations of velocities/accelerations. And control inputs are velocities or accelerations with or without bounds where, for the low level control of motors, velocity-servo modules or torque-servo modules are used to generate desired control inputs. However, WMR systems have motor armature current constraint as well as battery voltage constraint in practice. Also, since final control inputs are voltages (PWM duty ratios) generated by those servo modules, there may exist bad cases where those modules cannot track the desired velocity/acceleration commands due to current and voltage constraints. Hence, efficient control algorithm for WMR systems considering those constraints is essentially required. Based on above statements, we will study TP and TF for WMRs to move fast considering dynamics with current and voltage constraints. Obstacles are not considered explicitly. Instead, we consider the bound of path-deviation, which limits deviations from the given configuration, and hence obstacles can be avoided.
For TF, an off-line minimum-time velocity control algorithm (TF-MV) is developed considering all constraints of each step. However, the TF-MV algorithm is complex and slow for real-time TF for WMR system. For this reason, we will propose an on-line near minimum-time TF algorithm (TF-NV) based on maximally scaling in the first control step solved from inverse model, which is simple but yields good performance close to minimum-time control with regard to the number of steps. The comparison of performances will be discussed with various simulations.
For TP, firstly, a near minimum-time control algorithm (TP-ND) is proposed satisfying current and voltage constraints and path-deviation requirement with search for two control parameters (number of steps for RS $M_R$ and velocity scale factor β). Secondly, with simplification which sets motor armature inductance $L_a$ to zero and with assumption of fixed translational velocity in RS, a minimum-time control algorithm (TP-MDFS) is proposed, where the fixed velocity is characterized by velocity scale factor $S_M$. Also, a near minimum-time piecewise constant voltage-controlled algorithm (TP-NDPS) is proposed in which there is no assumption of fixed velocity, nor is consideration of current constraint.
After planning of each constant voltage inputs, integrating procedure is performed by searching for time intervals and optimal radius scale factor $S_R$. In those TP algorithms, normalized voltages which will be applied to both motors are controlled directly without velocity-servo or torque-servo module, while satisfying the current constraints (except TP-NDPS), and each velocity scale factor is determined with binary search to improve the speed of search. Performances of TP algorithms will be compared with a conventional path-planning method.
Finally, three TP algorithms for compounded configuration will be considered where at least two rotational sections are necessary, based on the piecewise constant voltage method in TP-NDPS algorithm for primary configuration.
