  Limitations in actuation, sensing, and computation have forced small legged
robots to rely on carefully tuned, mechanically mediated leg trajectories for
effective locomotion. Recent advances in manufacturing, however, have enabled
the development of small legged robots capable of operation at multiple stride
frequencies using multi-degree-of-freedom leg trajectories. Proprioceptive
sensing and control is key to extending the capabilities of these robots to a
broad range of operating conditions. In this work, we use concomitant sensing
for piezoelectric actuation with a computationally efficient framework for
estimation and control of leg trajectories on a quadrupedal microrobot. We
demonstrate accurate position estimation (< 16% root-mean-square error) and
control (16% root-mean-square tracking error) during locomotion across a wide
range of stride frequencies (10-50 Hz). This capability enables the exploration
of two bioinspired parametric leg trajectories designed to reduce leg slip and
increase locomotion performance (e.g., speed, cost-of-transport, etc.). Using
this approach, we demonstrate high performance locomotion at stride frequencies
of (10-30 Hz) where the robot's natural dynamics result in poor open-loop
locomotion. Furthermore, we validate the biological hypotheses that inspired
the our trajectories and identify regions of highly dynamic locomotion, low
cost-of-transport (3.33), and minimal leg slippage (< 10%).
