Novel algorithmic advances have paved the way for robotics to transform the dynamics of many social and enterprise applications. To achieve true autonomy, robots need to continuously process and interact with their environment through computationally-intensive motion planning and control algorithms under a low power budget. Specialized architectures offer a potent choice to provide low-power, high-performance accelerators for these algorithms. Instead of taking a traditional route which profiles and maps hot code regions to accelerators, this paper delves into the algorithmic characteristics of the application domain. We observe that many motion planning and control algorithms are formulated as a constrained optimization problems solved online through Model Predictive Control (MPC). While models and objective functions differ between robotic systems and tasks, the structure of the optimization problem and solver remain fixed. Using this theoretical insight, we create RoboX, an end-to-end solution which exposes a high-level domain-specific language to roboticists. This interface allows roboticists to express the physics of the robot and its task in a form close to its concise mathematical expressions. The RoboX backend then automatically maps this high-level specification to a novel programmable architecture, which harbors a programmable memory access engine and compute-enabled interconnects. Hops in the interconnect are augmented with simple functional units that either operate on in-fight data or are bypassed according a micro-program. Evaluations with six different robotic systems and tasks show that RoboX provides a 29.4X (7.3X) speedup and 22.1X (79.4X) performance-per-watt improvement over an ARM Cortex A57 (Intel Xeon E3). Compared to GPUs, RoboX attains 7.8X, 65.5X, and 71.�8 higher Performance-per-Watt to Tegra X2, GTX 650 Ti, and Tesla K40 with a power envelope of only 3.4 Watts at 45 nm.