# Motion Planning for Mobile Robot with Modified BIT+
###### Abstract  
In this paper, a mobile robot motion planning method with modified BIT* (batch informed trees) and MPC (Model Predictive Control) is presented. The conventional BIT* was modified here by integrating a stretch method that improves the path points connections, to get a collision-free path more quickly. After getting a reference path, the MPC method is employed to determine the motion at each moment with a given objective function. In the objective function, a repulsive function based on the direction and distance of the obstacles is introduced to avoid the robot being too close to the obstacle, so the safety can be ensured. Simulation results show the good navigation performance of the whole framework in different scenarios. mobile robot; sampling-based planning; motion planning; BIT*; MPC +
Footnote †: _Applied_  
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Footnote †: It has been demonstrated that the path generated by RRT-based algorithm is suboptimal [8]. However, in RRT-based methods, the sampling points are randomly generated and there are a lot of unnecessary exploring, which leads to the inefficiency. Based on RRT, a lot of optimal planning algorithms have been developed. RRT* uses a predefined cost function to select the node with the lowest cost as the parent node [9]. After each iteration, the nodes on the existing tree will be reconnected, so as to ensure the computational complexity and asymptotically optimality. An extension of RRT* called RRT*-smart is proposed in [10], which can accelerate the convergence rate by optimizing the path and sampling in a smarter way. RRT*-connect proposed in [11] unifies the RRT-connect and RRT*. It's optimality has been demonstrated in the paper and some real implementations show good performance of this algorithm. Sampling-based A* [12], applies the idea of sampling to the classic graph-search algorithm A*. A heuristic function is used to optimize the connection strategy, which makes the search biased to the target state area. FMT* (Fast Marching Tree) [13] combines the advantages of RRT and PRM algorithm, and it can get better solutions than RRT* with fast convergence rate. However, in these methods, the generated sample points do not always improve the current path solution. Informed RRT* [14] firstly uses RRT* to get a initial path, and then transform all the next samples into an ellipsoid which is determined by the start state, goal state and path cost. The nodes sampled in this ellipsoid is proved to be able to improve the path so the asymptotically optimality is guaranteed. BIT* (batch informed trees) [15] get path nodes in a batch of samples using the heuristic function as in A* and find path solution with a serious of batches. Every exploring in the map is ensured to improve the current path quality. Informed RRT* and BIT* both improve the path continuously through iterations. But, once the cost of initial path solution is large, the convergence may slow down. Motivated by these two methods, we use the sampling strategy of informed RRT* in the process of BIT*. Then a stretch method is combined with BIT* algorithm, which can reduce the cost of initial path and further constrain the sampling area to deal with the randomness of sampling more effectively, speeding up the convergence rate. After getting a reference path, trajectory tracking plays an important role in navigating the mobile robot. The objective of trajectory tracking is to make the robot tracking the reference path with appropriate speed. In recent years, MPC-based method is widely used in trajectory tracking and motion control of mobile robots. According to the system model and current state, MPC predicts the future state for a period of time, and then solves an optimization problem to obtain the optimal control input. MPC can also be used to reduce energy consumption from the actuator [16]. In [17], a global reference path is generated by potential field method. Kinematic controller as well as dynamics controller were designed for motion control and trajectory tracking.