🤖 AI Summary
This paper addresses multi-task robotic manipulation in semi-structured environments containing both static and dynamic obstacles, where joint optimization of task sequencing and goal configuration poses severe computational challenges for conventional RTSP-based planners—often leading to timeout failures or low-quality solutions.
Method: We propose a novel online multi-query task-sequence planning framework that, for the first time in robotics, incorporates an approximation of the ε-Gromov–Hausdorff distance to enable joint task-configuration subspace decomposition and approximate isometric embedding. This yields a theoretically bounded subspace path stitching mechanism that guarantees bounded suboptimality while generating smooth trajectories.
Results: Experiments demonstrate a threefold speedup over baseline planners, a fivefold reduction in maximum trajectory jerk, and significant improvements in real-time performance and motion smoothness.
📝 Abstract
Robotic manipulator applications often require efficient online motion planning. When completing multiple tasks, sequence order and choice of goal configuration can have a drastic impact on planning performance. This is well known as the robot task sequencing problem (RTSP). Existing general-purpose RTSP algorithms are susceptible to producing poor-quality solutions or failing entirely when available computation time is restricted. We propose a new multi-query task sequencing method designed to operate in semi-structured environments with a combination of static and non-static obstacles. Our method intentionally trades off workspace generality for planning efficiency. Given a user-defined task space with static obstacles, we compute a subspace decomposition. The key idea is to establish approximate isometries known as $epsilon$-Gromov-Hausdorff approximations that identify points that are close to one another in both task and configuration space. Importantly, we prove bounded suboptimality guarantees on the lengths of paths within these subspaces. These bounding relations further imply that paths within the same subspace can be smoothly concatenated, which we show is useful for determining efficient task sequences. We evaluate our method with several kinematic configurations in a complex simulated environment, achieving up to 3x faster motion planning and 5x lower maximum trajectory jerk compared to baselines.
