Autonomous Mobile Robots (AMRs) operate on battery power, making energy efficiency a critical consideration, particularly in outdoor environments where terrain variations affect energy consumption. While prior research has primarily focused on computing energy-efficient paths from a source to a destination, these approaches often overlook practical scenarios where a robot needs to pick up an object en route - an action that can significantly impact energy consumption due to changes in payload. This paper introduces the Object-Pickup Minimum Energy Path Problem (OMEPP), which addresses energy-efficient route planning for AMRs required to pick up an object from one of many possible locations and deliver it to a destination. To address OMEPP, we first introduce a baseline algorithm that employs the Z star algorithm, a variant of A star tailored for energy-efficient routing, to iteratively visit each pickup point. While this approach guarantees optimality, it suffers from high computational cost due to repeated searches at each pickup location. To mitigate this inefficiency, we propose a concurrent PCPD search that manages multiple Z star searches simultaneously across all pickup points. Central to our solution is the Payload-Constrained Path Database (PCPD), an extension of the Compressed Path Database (CPD) that incorporates payload constraints. We demonstrate that PCPD significantly reduces branching factors during search, improving overall performance. Although the concurrent PCPD search may produce slightly suboptimal solutions, extensive experiments on real-world datasets show it achieves near-optimal performance while being one to two orders of magnitude faster than the baseline algorithm.