Chance-Constrained Motion Planning using Modeled Distance-to-Collision Functions

This paper introduces Chance Constrained Gaussian Process-Motion Planning (CCGP-MP), a motion planning algorithm for robotic systems under motion and state estimate uncertainties. The papers key idea is to capture the variations in the distance-to-collision measurements caused by the uncertainty in state estimation techniques using a Gaussian Process (GP) model. We formulate the planning problem as a chance constraint problem and propose a deterministic constraint that uses the modeled distance function to verify the chance-constraints. We apply Simplicial Homology Global Optimization (SHGO) approach to find the global minimum of the deterministic constraint function along the trajectory and use the minimum value to verify the chance-constraints. Under this formulation, we can show that the optimization function is smooth under certain conditions and that SHGO converges to the global minimum. Therefore, CCGP-MP will always guarantee that all points on a planned trajectory satisfy the given chance-constraints. The experiments in this paper show that CCGP-MP can generate paths that reduce collisions and meet optimality criteria under motion and state uncertainties. The implementation of our robot models and path planning algorithm can be found on GitHub.

Motion Planning Transformers: One Model to Plan Them All

Transformers have become the powerhouse of natural language processing and recently found use in computer vision tasks. Their effective use of attention can be used in other contexts as well, and in this paper, we propose a transformer-based approach for efficiently solving the complex motion planning problems. Traditional neural network-based motion planning uses convolutional networks to encode the planning space, but these methods are limited to fixed map sizes, which is often not realistic in the real-world. Our approach first identifies regions on the map using transformers to provide attention to map areas likely to include the best path, and then applies local planners to generate the final collision-free path. We validate our method on a variety of randomly generated environments with different map sizes, demonstrating reduction in planning complexity and achieving comparable accuracy to traditional planners.

Dynamically Constrained Motion Planning Networks for Non-Holonomic Robots

Reliable real-time planning for robots is essential in todays rapidly expanding automated ecosystem. In such environments, traditional methods that plan by relaxing constraints become unreliable or slow-down for kinematically constrained robots. This paper describes the algorithm Dynamic Motion Planning Networks (Dynamic MPNet), an extension to Motion Planning Networks, for non-holonomic robots that address the challenge of real-time motion planning using a neural planning approach. We propose modifications to the training and planning networks that make it possible for real-time planning while improving the data efficiency of training and trained models generalizability. We evaluate our model in simulation for planning tasks for a non-holonomic robot. We also demonstrate experimental results for an indoor navigation task using a Dubins car.