  Safe robot motion generation is critical for practical applications from
manufacturing to homes. In this work, we proposed a stochastic
optimization-based motion generation method to generate collision-free and
time-optimal motion for the articulated robot represented by composite signed
distance field (SDF) networks. First, we propose composite SDF networks to
learn the SDF for articulated robots. The learned composite SDF networks
combined with the kinematics of the robot allow for quick and accurate
estimates of the minimum distance between the robot and obstacles in a batch
fashion. Then, a stochastic optimization-based trajectory planning algorithm
generates a spatial-optimized and collision-free trajectory offline with the
learned composite SDF networks. This stochastic trajectory planner is
formulated as a Bayesian Inference problem with a time-normalized Gaussian
process prior and exponential likelihood function. The Gaussian process prior
can enforce initial and goal position constraints in Configuration Space.
Besides, it can encode the correlation of waypoints in time series. The
likelihood function aims at encoding task-related cost terms, such as collision
avoidance, trajectory length penalty, boundary avoidance, etc. The kernel
updating strategies combined with model-predictive path integral (MPPI) is
proposed to solve the maximum a posteriori inference problems. Lastly, we
integrate the learned composite SDF networks into the trajectory planning
algorithm and apply it to a Franka Emika Panda robot. The simulation and
experiment results validate the effectiveness of the proposed method.
