Survey of Robot 3D Path Planning Algorithms <s> Definition 5. <s> A unified approach suitable for path planning with moving polyhedral obstacles is presented. The planner views the space-time configuration of free space as disjoint polytopes that represent a time-dependent environment consisting of moving and stationary objects. Each point in the space-time domain is mapped into a unique polytope set. The planner then constructs a family of feasible collision-free trajectories by searching connected polytopes between the start polytope and the goal polytope that satisfy the speed and time constraints. Finally, a near-optimal trajectory is determined by constrained optimization. This approach does not require that obstacles be nonoverlapping or noncolliding. In addition, the obstacle is allowed to move faster than the planned robot. However, the speed of the obstacle must be piecewise-constant. The proposed approach can be easily extended to motion planning in higher dimensional spaces. > <s> BIB001 </s> Survey of Robot 3D Path Planning Algorithms <s> Definition 5. <s> We address optimal path planning in three dimensional space for an unmanned aerial vehicle (UAV) in the stationary risk environment. We separate the task into two stage, in the first one we determine the risk optimal 2D path for fixed time problem. Then we solve the series of BVPs (Boundary Value Problems) with different UAV speeds and determine the admissible 2D path, which satisfies the time and risk constraints. In the last step one takes into account the relief along the chosen path and determine the approximated 3D path, which minimizes 2D threat along the path and satisfies other constraints. <s> BIB002 </s> Survey of Robot 3D Path Planning Algorithms <s> Definition 5. <s> A flatness-based flight trajectory planning/replanning strategy is proposed for a quadrotor unmanned aerial vehicle (UAV). In the nominal situation (fault-free case), the objective is to drive the system from an initial position to a final one without hitting the actuator constraints while minimizing the total time of the mission or minimizing the total energy spent. When actuator faults occur, fault-tolerant control (FTC) is combined with trajectory replanning to change the reference trajectory in function of the remaining resources in the system. The approach employs differential flatness to express the control inputs to be applied in the function of the desired trajectories and formulates the trajectory planning/replanning problem as a constrained optimization problem. <s> BIB003
Trajectory planning assumes output to be time continuous and must be able to ensure control limitation, which is still a part of the whole path. According to Definition 5 above, local mathematic optimization methods also partly belong to path planning field. Authors in BIB001 transformed kinodynamic constraints into a bound of linear or nonlinear constraints and then used mathematic programming methods to find the bounded optimal path. Miller et al. BIB002 modeled the path planning problem in an optimal control form, which combines cost criterion and Hamiltonian function to form a boundary value problem (BVP) to find a realistic optimal path globally. Chamseddine et al. BIB003 introduced flatness based method to linearize the nonlinear bounds into polynomial form, and a bang-bang control is employed to generate a global optimal path. Other mathematic optimization methods such as level set method and support vector machine method also belong to this kind.