Image-based control (IBC) systems are common in many modern applications. In such systems, image-based sensing imposes massive compute workload, making them challenging to implement on embedded platforms. Approximate image processing is a way to handle this challenge. In essence, approximation reduces the workload at the cost of additional sensor noise. In this work, we propose an approximation-aware design approach for optimizing the energy, memory and performance of an IBC system, making it suitable for embedded implementation. First, we perform compute- and data-centric approximations and evaluate its impact on the energy efficiency, memory utilization and closed-loop quality-of-control (QoC) of the IBC system. We observe that the workload reductions due to approximations allow mapping these lighter approximated IBC tasks to embedded platforms with lower power consumption while still ensuring proper system functionality. Therefore, we explore the interplay between approximations and platform mappings to improve the energy-efficiency of IBC systems. Further, an IBC system operates under several environmental scenarios e.g., weather conditions. We evaluate the sensitivity of the IBC system to our approximation-aware design approach when operated under different scenarios and perform a failure probability (FP) analysis using Monte-Carlo simulations to analyze the robustness of the approximate system. Finally, we design an optimal approximation-aware controller that models the approximation error as sensor noise and show QoC improvements. We demonstrate the effectiveness of our approach using a concrete case-study of a lane keeping assist system (LKAS) using a heterogeneous NVIDIA AGX Xavier embedded platform in a hardware-in-the-loop (HiL) framework. We show energy and memory reduction of up to 92% and 88% respectively, for 44% QoC improvements with respect to the accurate implementation. We show that our approximation-aware design approach has an FP (per km) ≤ 9.6 × 10−6%.