In view of the shortcomings of low search efficiency and many path turning points of Probabilistic Roadmaps (PRM), a bidirectional search PRM global path planning algorithm is proposed. The algorithm improves the search connection rules by using the positive and negative directions to search the path alternately, so that the connection of unnecessary nodes reduces, thereby speeding up the efficiency of path planning. Besides, the algorithm incorporates cubic spline interpolation. That will increase the smoothness of path planning and ensure that the mobile robot can realize the path planning task more smoothly and safely. The simulation results show that the improved algorithm can effectively improve the convergence speed and path smoothness of the algorithm. Finally, the improved algorithm is applied to the actual mobile robot navigation experiment. The experimental results have proven that the path planning strategy was able to a superior advantage over traditional PRM in path quality and computational time.

The consensus control problem of multi-agent systems (MASs) is studied. Firstly, a predefined-time consensus control algorithm is proposed for nonlinear uncertain systems with the input delay and switching topology. Then, the problem of resource consumption is considered, a dynamic eventtriggered predefined-time consensus control algorithm is presented by introducing internal dynamic variables, which can make the MASs achieve consensus in the preset time. The correctness of the algorithm is proved by algebraic graph theory and Lyapunov theory, and there is no Zeno behavior. Simulation comparison experiments verify the effectiveness and superiority of the proposed algorithm. Compared with the finite-time control algorithm, the convergence time of this algorithm is independent of the initial state. The upper bound of the system convergence time can be set by selecting a time parameter. Compared with the fixed-time control algorithm, the convergence time of this algorithm is independent of the controller parameters, only related to a single parameter, the setting is simple, and the estimated convergence time is less conservative. Compared with the static triggering mechanism, the dynamic triggering mechanism can avoid a large number of triggering.INDEX TERMS Multi-agent systems (MASs), consensus control, the nonlinear uncertain system, input delay, switching topologies, dynamic event-triggered control, predefined-time consensus control