## LaValle Planning Algorithms, ch 8

• (304) Since paths as discussed are simply a sequence of configurations, some method must be used to ensure actions can be taken to cause that sequence of configurations
• It may not be possible to actually achieve that sequence
• What happens why noise disrupts expectations?
• (305) Can try and use ctrl thry to deal w/ uncertainty
• (306) Discrete optimal feedback planning is under discrete state/action sets (state can be continuous though)
• (307) A feasible plan (policy) is one that directs planning to goal state for all configurations
• (309) Basically rehashing RL, but w/o noise
• (312) For maximum clearance, propogate values in waves out from obstacles, and follow skeleton
• (318) Given a vector fielad & starting pt, traj represents an integral curve of a differential eq
• Can have discontinuities, called hybrid systems in ctrl thry (I think this is also what mixed discrete/continuous is called)
• (325) A tangent space on an n-dim manifold is a hyperplane R^m that best approximates the the manifold at a point, related directly to the derivative
• (328) A vector field defines tangent spaces all over the surface of a manifold, defines n differential eqs, defines a solution traj from any pt on the manifold
• In feedback motion planning, a path must be found, if one exists or must report failure if one doesn’t
• No initial condition, solution vector field instead of solution path
• (329) Vector fields that have a solution pt only converge asymptotically to the pt
• Can instead use unit speed everywhere except at the goal to have finitie-time convergence, but this may not always be possible to execute in a real system.
• (330) Feasible feedback motion planning can be made optimal w/addition of cost function
• Vector field can be defined as the negative gradient of the cost function
• Related to LQR
• (332) Planning over a cell-decomposed space works by
• Doing complete planning across cells
• Defining a vec field on each n-cell, vector field should cause flow according to discrete plan
• (340) Using funnels.  Should have superstates and superactions, because they overlap
• (342) Once funnels have been laid out, chosing the sequence of funnels to take is another discrete planning problem
• (343) Can also do sample based methods, seems efficient
• (346) VI for continuous state, discrete action
• (348) VI for continuous state, action
• (350) Using a timestep in VI is counter to most motion planning algs that work over continuous time
• Approximating with discrete time isn’t so bad for regular motion planning, but causes trouble in dynamic motion planning
• Stochasticity
• (352) VI and tracking states that can have values that possibly change
• (353) Dijkstra-like continuous state algo
• Intermediary values in Dijkstra and VI are different but end result is same
• (354) Wave-front propagation