Reverse iteration of planning data for system control

A non-transitory computer-readable storage medium having stored therein instructions, that when executed by a computing device, cause the computing device to perform functions for planning balloon flight states configured to cause at least one balloon to fly substantially along a predicted path, the functions comprising:

• receiving a specification for N time steps at which to compute N corresponding contingency tables of contingent balloon flight states for the at least one balloon, wherein the N time steps define a sequence of time steps in a range between an initial time and a target time;
• reverse-accessing the N contingency tables in an order from the initial time to the target time by using an iterator function configured for recursively determining the contingency tables at successive time steps in a computational iteration order from the target time to the initial time;
• for the at least one balloon, determining a sequence of planned balloon flight states from the reverse-accessed contingency tables, ordered from the initial time to the target time, corresponding to a predicted balloon flight trajectory that is within a threshold of a quantitative flight-plan objective;
• and
• causing the at least one balloon to execute at least one flight command from the determined sequence of planned balloon flight states, to cause the at least one balloon to attempt to follow at least a portion of the predicted flight trajectory,
• wherein reverse-accessing the N contingency tables in the order from the initial time to the target time is achieved in O(N log2 N) iterations using memory for O(log2 N) contingency tables, and comprises:
• recursively (i) subdividing the sequence of time steps by a factor of at least two into successively smaller sub-sequences, (ii) iterating in the computational iteration order over each recursively subdivided sub-sequence, and (iii) accessing a contingency table closest in time to the initial time for the recursive iteration over each recursively subdivided sub-sequence.

A system for planning balloon flight states configured to cause at least one balloon to fly substantially along a predicted path, the system comprising:

• at least one processor;
• and
• data storage comprising program instructions executable by the at least one processor to cause the system to perform functions comprising:
• receiving a specification for N time steps at which to compute N corresponding contingency tables of contingent balloon flight states for the at least one balloon, wherein the N time steps define a sequence of time steps in a range between an initial time and a target time;
• reverse-accessing the N contingency tables in an order from the initial time to the target time by using an iterator function configured for recursively determining the contingency tables at successive time steps in a computational iteration order from the target time to the initial time;
• for the at least one balloon, determining a sequence of planned balloon flight states from the reverse-accessed contingency tables, ordered from the initial time to the target time, corresponding to a predicted balloon flight trajectory that is within a threshold of a quantitative flight-plan objective;
• and
• causing the at least one balloon to execute at least one flight command from the determined sequence of planned balloon flight states, to cause the at least one balloon to attempt to follow at least a portion of the predicted flight trajectory,
• wherein reverse-accessing the N contingency tables in the order from the initial time to the target time is achieved in O(N log2 N) iterations using memory for O(log2 N) contingency tables, and comprises:
• recursively (i) subdividing the sequence of time steps by a factor of at least two into successively smaller sub-sequences, (ii) iterating in the computational iteration order over each recursively subdivided sub-sequence, and (iii) accessing a contingency table closest in time to the initial time for the recursive iteration over each recursively subdivided sub-sequence.