RoboPrec: Enabling Reliable Embedded Computing for Robotics by Providing Accuracy Guarantees Across Mixed-Precision Datatypes

Abstract

Mobile robots demand power efficiency as well as accuracy and high performance in their computations. Embedded microcontrollers and FPGAs can consume as much as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1000\times$</tex-math></inline-formula> less power than large CPUs and GPUs, however, these power-efficient platforms often lack full floating-point support and rely on fixed-point computations to deliver performance. This is a challenge as most robotics software uses floating-point datatypes (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double</i>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">float</i>) to conservatively ensure accuracy, and prior works that use fixed-point types employ unreliable ad hoc approaches to select the datatype precision (i.e., quantity and allocation of bits). We address this challenge with the RoboPrec framework, where we: (i) develop a transpiler that integrates code transformations and robot-specific code generation with traditional numerical stability analysis methods (which calculate error bounds), and adapts them to be practical for robotics software; and then leverage this to (ii) generate guaranteed-accuracy fixed-point code that is deployable to embedded computing platforms. We use rigid body dynamics, a fundamental robotics workload, as a motivating case study. We find that RoboPrec-generated 32-bit fixed-point code can be up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$8\times$</tex-math></inline-formula> faster than <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">float</i> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$122\times$</tex-math></inline-formula> faster than <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double</i> on embedded processors while, critically, also providing guaranteed accuracy bounds with lower worst-case error than <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">float</i>.