  Dexterous manipulation, particularly adept coordinating and grasping,
constitutes a fundamental and indispensable capability for robots, facilitating
the emulation of human-like behaviors. Integrating this capability into robots
empowers them to supplement and even supplant humans in undertaking
increasingly intricate tasks in both daily life and industrial settings.
Unfortunately, contemporary methodologies encounter serious challenges in
devising manipulation trajectories owing to the intricacies of tasks, the
expansive robotic manipulation space, and dynamic obstacles. We propose a novel
approach, APEX, to address all these difficulties by introducing a
collision-free latent diffusion model for both robotic motion planning and
manipulation. Firstly, we simplify the complexity of real-life ambidextrous
dual-arm robotic manipulation tasks by abstracting them as aligning two
vectors. Secondly, we devise latent diffusion models to produce a variety of
robotic manipulation trajectories. Furthermore, we integrate obstacle
information utilizing a classifier-guidance technique, thereby guaranteeing
both the feasibility and safety of the generated manipulation trajectories.
Lastly, we validate our proposed algorithm through extensive experiments
conducted on the hardware platform of ambidextrous dual-arm robots. Our
algorithm consistently generates successful and seamless trajectories across
diverse tasks, surpassing conventional robotic motion planning algorithms.
These results carry significant implications for the future design of diffusion
robots, enhancing their capability to tackle more intricate robotic
manipulation tasks with increased efficiency and safety. Complete video
demonstrations of our experiments can be found in
https://sites.google.com/view/apex-dual-arm/home.
