  Sampling-based motion planning under task constraints is challenging because
the null-measure constraint manifold in the configuration space makes rejection
sampling extremely inefficient, if not impossible. This paper presents a
learning-based sampling strategy for constrained motion planning problems. We
investigate the use of two well-known deep generative models, the Conditional
Variational Autoencoder (CVAE) and the Conditional Generative Adversarial Net
(CGAN), to generate constraint-satisfying sample configurations. Instead of
precomputed graphs, we use generative models conditioned on constraint
parameters for approximating the constraint manifold. This approach allows for
the efficient drawing of constraint-satisfying samples online without any need
for modification of available sampling-based motion planning algorithms. We
evaluate the efficiency of these two generative models in terms of their
sampling accuracy and coverage of sampling distribution. Simulations and
experiments are also conducted for different constraint tasks on two robotic
platforms.
