Robotic computing at the edge needs to meet multiple constraints on power and form factor while delivering the required performance for power-hungry neural network kernels. This work proposed spiking neural network (SNN) alternatives and augmentations for algorithms and circuits for edge robots. We show SNN-driven locomotion for power-constrained hexapod robots, SNN-augmented target tracking for high-speed aerial robots and SNN-assisted visual navigation for size-critical micro-robots. The first part of the work extends rhythmic leg movement of insects to an SNN-based gait generator to demonstrate an online training method. We then utilize an event-based vision sensor as the sensory front-end to the hexapod locomotion to show the first spike-only closed-loop robotic platform. In the second part, we observe that SNN and event-camera forms a sensor-processor pair well-suited for high-speed processing while frame-camera with convolutional neural network (CNN) suits the applications with the high-accuracy requirement. This trade-off between accuracy vs. latency in the event and frame-based visual processing arises from the detailed temporal and spatial resolutions captured by event and frame cameras respectively. We utilize these complementary strengths to build high-speed target identification and tracking system with SNN providing high-speed but noisy target estimates with CNN preserving the lost accuracy by providing reliable periodic anchors. We build a heterogeneous SoC with low-power RRAM compute-in-memory mapping CNN and high-speed SRAM compute-near-memory accelerating SNN. The final part of the work generalizes the idea of multi-modal processing applied in the previous chapters to divide the robotic computing workloads between trainable-CNN for perception tasks and physics-based symbolic processing for motion encoding tasks. Our SoC uses RRAM compute-near-memory kernels to accelerate CNN-based perception while SRAM compute-in-memory carries out SNN-based localization on micro-robots. To summarize, this work attempted to substitute and augment the compute-constrained robotic hardware with SNN for energy saving and performance improvement.