An algorithm for finding the global maximum of a multimodal, multivariate function
Mathematical Programming: Series A and B
Robot Motion Planning
Planning Algorithms
Point-Based Value Iteration for Continuous POMDPs
The Journal of Machine Learning Research
Running the table: an AI for computer billiards
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Planning with continuous resources in stochastic domains
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Planning under continuous time and resource uncertainty: a challenge for AI
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
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We investigate search problems in continuous state and action spaces with no uncertainty. Actions have costs and can only be taken at discrete time steps (unlike the case with continuous control). Given an admissible heuristic function and a starting state, the objective is to find a minimum-cost plan that reaches a goal state. As the continuous domain does not allow the tight optimality results that are possible in the discrete case (for example by A*), we instead propose and analyze an approximate forward-search algorithm that has the following provable properties. Given a desired accuracy Ε, and a bound d on the length of the plan, the algorithm computes a lower bound L on the cost of any plan. It either (a) returns a plan of cost L that is at most Ε more than the optimal plan, or (b) if, according to the heuristic estimate, there may exist a plan of cost L of length d, returns a partial plan that traces the first d steps of such plan. To our knowledge, this is the first algorithm that provides optimality guarantees in continuous domains with discrete control and without uncertainty.