  This paper develops a path planner that minimizes risk (e.g. motion
execution) while maximizing accumulated reward (e.g., quality of sensor
viewpoint) motivated by visual assistance or tracking scenarios in unstructured
or confined environments. In these scenarios, the robot should maintain the
best viewpoint as it moves to the goal. However, in unstructured or confined
environments, some paths may increase the risk of collision; therefore there is
a tradeoff between risk and reward. Conventional state-dependent risk or
probabilistic uncertainty modeling do not consider path-level risk or is
difficult to acquire. This risk-reward planner explicitly represents risk as a
function of motion plans, i.e., paths. Without manual assignment of the
negative impact to the planner caused by risk, this planner takes in a
pre-established viewpoint quality map and plans target location and path
leading to it simultaneously, in order to maximize overall reward along the
entire path while minimizing risk. Exact and approximate algorithms are
presented, whose solution is further demonstrated on a physical tethered aerial
vehicle. Other than the visual assistance problem, the proposed framework also
provides a new planning paradigm to address minimum-risk planning under
dynamical risk and absence of substructure optimality and to balance the
trade-off between reward and risk.
