  In this paper, we consider a general task of jumping varying distances and
heights for a quadrupedal robot in noisy environments, such as off of uneven
terrain and with variable robot dynamics parameters. To accurately jump in such
conditions, we propose a framework using deep reinforcement learning that
leverages and augments the complex solution of nonlinear trajectory
optimization for quadrupedal jumping. While the standalone optimization limits
jumping to take-off from flat ground and requires accurate assumptions of robot
dynamics, our proposed approach improves the robustness to allow jumping off of
significantly uneven terrain with variable robot dynamical parameters and
environmental conditions. Compared with walking and running, the realization of
aggressive jumping on hardware necessitates accounting for the motors'
torque-speed relationship as well as the robot's total power limits. By
incorporating these constraints into our learning framework, we successfully
deploy our policy sim-to-real without further tuning, fully exploiting the
available onboard power supply and motors. We demonstrate robustness to
environment noise of foot disturbances of up to 6 cm in height, or 33% of the
robot's nominal standing height, while jumping 2x the body length in distance.
