LaValle Planning Algorithms, ch 14


  • (682) Sample-based planning under differential constraints
  • (660) Completeness analysis begins w/considering pts that can be reached by integrating action trajectories
  • (661) Have forward a& backward time-reachable sets
  • (663) Under differential constraints, sample-based motion planning algs work by sampling the space of action trajectories
  • Discrete time model discretizes actions as well(?)
  • (664) Reachability trees/graphs
    • (665) Merging nodes/structure depends heavily on time discretization
    • (666) No guarantee planning will ever end up in same state twice, leading to inneficiency
  • (668) Use of motion planning primitives can be modeled as a hybrid system
  • (672) Planning using a simulator
  • (673) Euler, Runge-Kutta, & other integration approximation methods
  • (676) Local planning w/differential constraints is generally very difficult
  • Can allow approximate navigation to a point in configuration space
  • (689) RDTs were originally designed for planning under differential constraints
    • Can be considered a subgraph of the reachability graph under some method of discretization
  • (690) Problems of RDTs in differential settings w/obstacles
  • Problem as w/ most differential planners is connecting nearby states
  • (696) Can try “plan and transform” – plan in a simple case (such as under no differential constraints) and then modify plan if it violates some constraints
  • (707) Traj optimization takes an existing traj and optimizes some characteristic of it, can be time to execute a path, or even smoothing out paths that have lots of kinks (such as from RDTs)
    • In the general case this is a hard problem
  • (708) Can be done by grad descent on cost
  • (709) Methods that utilize repeated small perturbations requires integration and collision checking, which can be expensive
  • Traj optimization can get stuck in local optima
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