Generating and scheduling activities is particularly challenging
 when considering both consumptive resources and
 complex resource interactions such as time-dependent resource
 usage.We present three methods of determining valid
 temporal placement intervals for an activity in a temporally
 grounded plan in the presence of such constraints. We introduce
 the Max Duration and Probe algorithms which are
 sound, but incomplete, and the Linear algorithm which is
 sound and complete for linear rate resource consumption.
 We apply these techniques to the problem of scheduling
 awakes for a planetary rover where the awake durations
 are affected by existing activities. We demonstrate how the
 Probe algorithm performs competitively with the Linear algorithm
 given an advantageous problem space and well-defined
 heuristics. We show that the Probe and Linear algorithms
 outperform the Max Duration algorithm empirically.
 We then empirically present the runtime differences between
 the three algorithms. The Probe algorithm is currently base-lined
 for use in the onboard scheduler for NASA’s next planetary
 rover, the Mars 2020 rover.
This paper describes and analyzes three methods to schedule non-fixed duration activities in the presence of consumptive resources. The paper presents three approaches for on-board scheduling of activities in a planetary rover under reservoir resource constraints.