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This thesis investigates the analysis and optimization of safety and performance-critical computational tasks for autonomous robots, operating in unknown and unstructured environments with complex objectives under strict computational and power constraints. Our primary contribution is a novel safety-performance (SP) metric that emphasizes on safety while rewarding enhanced performance of real-time computational tasks, expanding the notion of nominal safety in the autonomous vehicle domain. We adopt the Stochastic Heterogeneous Parallel Directed Acyclic Graph (SHP-DAG) model to capture the uncertain nature of robotic applications and their required computations, modeling execution times using probability distributions instead of deterministic worst-case execution time (WCET). We argue that computational tasks enabling robotic autonomy, such as localization and mapping, path planning, task allocation, depth estimation, and optical flow, must be scheduled and optimized to guarantee timely and correct behavior while allowing for runtime reconfiguration of scheduling parameters. To attain computational awareness in autonomous robots, we conduct a data-driven study of these computational tasks from the resource management perspective, profiling and analyzing their timing, power, and memory performance across three embedded computing platforms. Our SP metric allows us to apply the schedulers First-In-First-Out (FIFO) and Completely Fair Scheduler (CFS) of the Linux kernel on complex robotic computational tasks and compare the SP metric with baseline metrics, such as average and worst-case makespan. Extensive experimental results on NVIDIA Jetson AGX Xavier hardware demonstrate the effectiveness of the proposed SP metric in managing computational tasks while balancing safety and performance in robotic systems. Our findings reveal a correlation between task performance and a robot's operational environment, which justifies the concept of computation-aware robots and highlights the importance of our work as a crucial step towards this goal. Finally, we also integrate a custom scheduler with the FIFO priorities with our SHP-DAG and show the efficacy of our framework in comparison to default fair scheduler. / Doctor of Philosophy / This paper explores how to improve the safety and performance of autonomous robots operating in unpredictable and complex environments. These robots need to carry out various tasks such as mapping, path planning, and depth estimation, while managing limited computing power and energy resources. To achieve this, we introduce a new safety-performance (SP) metric that prioritizes safety while rewarding better task performance. We use a cutting-edge model that captures the uncertainty of robotic tasks and their required computing resources. By doing so, we can better schedule and optimize these tasks to ensure timely and correct behavior while allowing for adjustments to scheduling parameters during operation. Our study investigates the performance of key computing tasks on various embedded computing platforms. By comparing our SP metric with traditional measures, we can demonstrate the effectiveness of our approach in managing these tasks while balancing safety and performance in robotic systems. We also do system integration of a real-time scheduler with robotic tasks, which shows the efficacy of our framework. Our findings show a connection between a robot's environment and its computing performance, highlighting the importance of our work as a critical step towards creating smarter and safer autonomous robots that can better adapt to their surroundings.