Online Motion Planning Over Multiple Homotopy Classes with Gaussian Process Inference

Abstract

Efficient planning in dynamic and uncertain environments is a fundamental challenge in robotics. In the context of trajectory optimization, the feasibility of paths can change as the environment evolves. Therefore, it can be beneficial to reason about multiple possible paths simultaneously. We build on prior work that considers graph-based trajectories to find solutions in multiple homotopy classes concurrently. Specifically, we extend this previous work to an online setting where the unreachable (in time) part of the graph is pruned and the remaining graph is reoptimized at every time step. As the robot moves within the graph on the path that is most promising, the pruning and reoptimization allows us to retain candidate paths that may become more viable in the future as the environment changes, essentially enabling the robot to dynamically switch between numerous homotopy classes. We compare our approach against prior work without the homotopy switching capability and show improved performance across several metrics in simulation with a 2D robot in multiple dynamic environments under noisy measurements and execution.

GPU Accelerated Batch Multi-Convex Trajectory Optimization for a Rectangular Holonomic Mobile Robot

“…The F T F needs to be computed only once since they do not change with iteration or batch index. Similar analysis can be drawn for (14) as well. Solutions of ( 15)-( 16) are available as symbolic formulae whose evaluation has linear complexity with respect to the number of footprint circles and obstacles.…”

“…Note: Unlike [13], [14], works like [11], [12] and ours do not explicitly search for solutions in different homotopy but rely on stochastic sampling to achieve that.…”

Online Trajectory Replanning for Sudden Environmental Changes During Automated Parking: A Parallel Stitching Method

“…4b, the replanned trajectory is not homotopic with the evasive trajectory. This means that our replanner can alter the homotopy class if a better one is found during the selection of a qualified connective trajectory [30,31]. This property allows the proposed replanner to improve the global optimality of the solution especially when the hybrid A* algorithm (or other sampling-and-search-based ones that do guarantee optimality) is involved in the replanning process.…”

Predicted Composite Signed-Distance Fields for Real-Time Motion Planning in Dynamic Environments

“…The first is to assume full prior knowledge of the moving obstacle trajectories in the scene [3]- [5]. The second approach is 'continuous re-planning' in which the motion planner either re-optimises and adapts the current planned trajectory, or considers multiple trajectory modes at any one time, such as in ITOMP [1], and smoothly switches between them as new information is provided [6], [7]. However, there have been few works that incorporate predicted obstacle motions into the motion planning of articulated systems.…”