  This work considers online optimal motion planning of an autonomous agent
subject to linear temporal logic (LTL) constraints. The environment is dynamic
in the sense of containing mobile obstacles and time-varying areas of interest
(i.e., time-varying reward and workspace properties) to be visited by the
agent. Since user-specified tasks may not be fully realized (i.e., partially
infeasible), this work considers hard and soft LTL constraints, where hard
constraints enforce safety requirement (e.g. avoid obstacles) while soft
constraints represent tasks that can be relaxed to not strictly follow user
specifications. The motion planning of the agent is to generate policies, in
decreasing order of priority, to 1) formally guarantee the satisfaction of
safety constraints; 2) mostly satisfy soft constraints (i.e., minimize the
violation cost if desired tasks are partially infeasible); and 3) optimize the
objective of rewards collection (i.e., visiting dynamic areas of more
interests). To achieve these objectives, a relaxed product automaton, which
allows the agent to not strictly follow the desired LTL constraints, is
constructed. A utility function is developed to quantify the differences
between the revised and the desired motion plan, and the accumulated rewards
are designed to bias the motion plan towards those areas of more interests.
Receding horizon control is synthesized with an LTL formula to maximize the
accumulated utilities over a finite horizon, while ensuring that safety
constraints are fully satisfied and soft constraints are mostly satisfied.
Simulation and experiment results are provided to demonstrate the effectiveness
of the developed motion strategy.
