Fully autonomous vehicles (AVs) must meet stringent real-time performance and safety-criticality constraints of multiple applications simultaneously in highly dynamic environmental conditions. To enable such a system, carefully selected accelerators and general-purpose cores on Systems-on-Chips (SoCs) are required. However, schedulers that are agnostic to this heterogeneity lead to inefficient utilization of hardware resources and increase the time to complete the AV's mission. As a solution, our letter proposes a heterogeneity-aware, multi-level scheduler called HetSched. HetSched leverages run-time information about the underlying heterogeneous SoC, along with the applications' real-time constraints to improve an AV's mission time. Our evaluation demonstrates a reduction in mission time of 2.0-4.8×, when compared against state-of-the-art (SOTA) schedulers. Furthermore, when used as part of an SoC design space exploration loop, in comparison to the SOTA schedulers, HetSched reduces the number of accelerators required by an SoC to safely complete the AV's mission by 1.9× on average.