Method, system and storage medium of resilient human-on-the-loop range-only cooperative positioning of plurality of unmanned aerial vehicles

A system, comprising:

• a memory, configured to store program instructions for performing a method of resilient human-on-the-loop range-only cooperative positioning of a plurality of unmanned aerial vehicles (UAVs);
• and
• a processor, coupled with the memory and, when executing the program instructions, configured for:
• determining an initial distribution, an initial policy, and a pre-defined tolerance value by a processer;
• computing an initial exploitability using the initial distribution and the initial policy;
• for an i-th iteration, for each time step, performing a forward updating of a distribution of a portion of the plurality of UAVs by computing a distribution of the portion of the plurality of UAVs at a k-th time step using a distribution of the portion of the plurality of UAVs at a (k−1)-th time step under a policy at the (k−1)-th time step;
• and performing a backward updating of a Q function of each UAV of the plurality of UAVs by computing a Q function value of each UAV of the plurality of UAVs at the k-th time step using a Q function value of each UAV of the plurality of UAVs at a (k+1)-th time step;
• for each time step, calculating a dual variable at an (i+1)-th iteration using a dual variable at the i-th iteration and the computed Q function value of each UAV of the plurality of UAVs at the i-th iteration;
• and calculating a policy at the (i+1)-th iteration using the calculated dual variable at the (i+1)-th iteration;
• computing an exploitability at the (i+1)-th iteration and a ratio of the exploitability at the (i+1)-th iteration over the initial exploitability;
• and
• if the ratio is less than or equal to the pre-defined tolerance value, maintaining a policy at the i-th iteration for each UAV of the plurality of UAVs;
• and if the ratio is greater than the pre-defined tolerance value, using the policy at the (i+1)-th iteration for each UAV of the plurality of UAVs.

A non-transitory computer-readable storage medium, containing program instructions for, when being executed by a processor, performing a method of resilient human-on-the-loop range-only cooperative positioning of a plurality of unmanned aerial vehicles (UAVs);

• the method comprising:
• determining an initial distribution, an initial policy, and a pre-defined tolerance value by a processer;
• computing an initial exploitability using the initial distribution and the initial policy;
• for an i-th iteration, for each time step, performing a forward updating of a distribution of a portion of the plurality of UAVs by computing a distribution of the portion of the plurality of UAVs at a k-th time step using a distribution of the portion of the plurality of UAVs at a (k−1)-th time step under a policy at the (k−1)-th time step;
• and performing a backward updating of a Q function of each UAV of the plurality of UAVs by computing a Q function value of each UAV of the plurality of UAVs at the k-th time step using a Q function value of each UAV of the plurality of UAVs at a (k+1)-th time step;
• for each time step, calculating a dual variable at an (i+1)-th iteration using a dual variable at the i-th iteration and the computed Q function value of each UAV of the plurality of UAVs at the i-th iteration;
• and calculating a policy at the (i+1)-th iteration using the calculated dual variable at the (i+1)-th iteration;
• computing an exploitability at the (i+1)-th iteration and a ratio of the exploitability at the (i+1)-th iteration over the initial exploitability;
• and
• if the ratio is less than or equal to the pre-defined tolerance value, maintaining a policy at the i-th iteration for each UAV of the plurality of UAVs;
• and if the ratio is greater than the pre-defined tolerance value, using the policy at the (i+1)-th iteration for each UAV of the plurality of UAVs.