Survey of Robot 3D Path Planning Algorithms <s> 6.3. <s> An available pressurized air source, such as an inflated tire, connectable by appropriate conduit means, with flow control and pressure regulation provisions, through an air transmitter or face mask, to the breathing passages of a passenger in a submerged land vehicle to either provide emergency breathing air for the passenger, or to fill an inflatable and portable air pack which the passenger may leave the vehicle with, or both. <s> BIB001 </s> Survey of Robot 3D Path Planning Algorithms <s> 6.3. <s> Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed-integer linear program (MILP). This can be solved using commercial software written for the operations research community. In the paper, an approximate model of aircraft dynamics using only linear constraints is developed, enabling the MILP approach to be applied to aircraft collision avoidance. The formulation can also be extended to include multiple waypoint path-planning, in which each vehicle is required to visit a set of points in an order chosen within the optimization. <s> BIB002 </s> Survey of Robot 3D Path Planning Algorithms <s> 6.3. <s> This paper presents several efficient solution techniques specific to the optimal path planning of an autonomous vehicle. Mixed-integer linear programming (MILP) is the underlying problem formulation, from which an optimal solution can be obtained through the use of a commercially available MILP solver such as CPLEX. The solution obtained is optimal in terms of the cost function specified in terms of fuel, time, altitude, etc. Several techniques are introduced to reduce the complexity of the underlying mathematical problems as to help make the path planning approach suitable for running in a mission-critical real-time environment. Some of these techniques may be applicable to other optimal path planning approaches. <s> BIB003 </s> Survey of Robot 3D Path Planning Algorithms <s> 6.3. <s> Abstract The home space for optimal control is a Sobolev space. The home space for pseudospectral theory is also a Sobolev space. It thus seems natural to combine pseudospectral theory with optimal control theory and construct “pseudospectral optimal control theory”, a term coined by Ross. In this paper, we review key theoretical results in pseudospectral optimal control that have proven to be critical for a successful flight. Implementation details of flight demonstrations onboard NASA spacecraft are discussed along with emerging trends and techniques in both theory and practice. The 2011 launch of pseudospectral optimal control in embedded platforms is changing the way in which we see solutions to challenging control problems in aerospace and autonomous systems. <s> BIB004
Analysis. This kind of methods maintains a complete form to describe the states and environmental variables, and when applied in 3D cluttered environments, these methods can adapt themselves by employing much more constraints according to the environments. These algorithms tend to have a much more complex formulation, that is, a heavy computational burden. There exists a method that can solve the weakness, that is, discrete decisions in an optimization procedure. The method allows problems to be solved on-line flexibly by devising the environment  BIB002 BIB003 . For example, Bellingham et al.  only used MILP to justify the local states and thus increase the whole exploring process a lot. Based on the analysis above, this paper provides a summarization in Table 4 . BIB004 , SeDuMi BIB001 , and so forth