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1. Robust Optimization-based Motion Planning for high-DOF Robots under Sensing Uncertainty

   https://doi.org/10.1109/ICRA48506.2021.9560917  

   Quintero-Pena, Carlos ; Kyrillidis, Anastasios ; Kavraki, Lydia E. ( May 2021 , 2021 IEEE International Conference on Robotics and Automation (ICRA))

   null (Ed.)

   Motion planning for high degree-of-freedom (DOF) robots is challenging, especially when acting in complex environments under sensing uncertainty. While there is significant work on how to plan under state uncertainty for low-DOF robots, existing methods cannot be easily translated into the high-DOF case, due to the complex geometry of the robot’s body and its environment. In this paper, we present a method that enhances optimization-based motion planners to produce robust trajectories for high-DOF robots for convex obstacles. Our approach introduces robustness into planners that are based on sequential convex programming: We reformulate each convex subproblem as a robust optimization problem that “protects” the solution against deviations due to sensing uncertainty. The parameters of the robust problem are estimated by sampling from the distribution of noisy obstacles, and performing a first-order approximation of the signed distance function. The original merit function is updated to account for the new costs of the robust formulation at every step. The effectiveness of our approach is demonstrated on two simulated experiments that involve a full body square robot, that moves in randomly generated scenes, and a 7-DOF Fetch robot, performing tabletop operations. The results show nearly zero probability of collision for a reasonable range of the noise parameters for Gaussian and Uniform uncertainty. 

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2. Efficient Robot Motion Planning via Sampling and Optimization

   https://doi.org/10.23919/ACC50511.2021.9483146  

   Leu, Jessica ; Zhang, Ge ; Sun, Liting ; Tomizuka, Masayoshi ( May 2021 , 2021 American Control Conference (ACC))

   null (Ed.)

   Robot motion planning is one of the important elements in robotics. In environments full of obstacles, it is always challenging to find a collision-free and dynamically feasible path between the robot's initial configuration and goal configuration. While many motion planning algorithms have been proposed in the past, each of them has its pros and cons. This work presents a benchmark which implements and compares existing planning algorithms on a variety of problems with extensive simulation. Based on that, we also propose a hybrid planning algorithm, RRT*-CFS, that combines the merits of sampling-based planning methods and optimization-based planning methods. The first layer, RRT*, quickly samples a semi-optimal path. The second layer, CFS, performs sequential convex optimization given the reference path from RRT*. The proposed RRT*-CFS has feasibility and convergence guarantees. Simulation results show that RRT*-CFS benefits from the hybrid structure and performs robustly in various scenarios including the narrow passage problems. 

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3. Stampede: A Discrete-Optimization Method for Solving Pathwise-Inverse Kinematics

   Rakita, Daniel ; Mutlu, Bilge ( May 2019 , 2019 International Conference on Robotics and Automation (ICRA))

   We present a discrete-optimization technique for finding feasible robot arm trajectories that pass through provided 6-DOF Cartesian-space end-effector paths with high accuracy, a problem called pathwise-inverse kinematics. The output from our method consists of a path function of joint-angles that best follows the provided end-effector path function, given some definition of ``best''. Our method, called Stampede, casts the robot motion translation problem as a discrete-space graph-search problem where the nodes in the graph are individually solved for using non-linear optimization; framing the problem in such a way gives rise to a well-structured graph that affords an effective best path calculation using an efficient dynamic-programming algorithm. We present techniques for sampling configuration space, such as diversity sampling and adaptive sampling, to construct the search-space in the graph. Through an evaluation, we show that our approach performs well in finding smooth, feasible, collision-free robot motions that match the input end-effector trace with very high accuracy, while alternative approaches, such as a state-of-the-art per-frame inverse kinematics solver and a global non-linear trajectory-optimization approach, performed unfavorably. 

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4. Hardness of Motion Planning with Obstacle Uncertainty in Two Dimensions

   https://doi.org/10.1177/0278364921992787  

   Shimanuki, Luke ; Axelrod, Brian ( September 2021 , The International Journal of Robotics Research)

   We consider the problem of motion planning in the presence of uncertain obstacles, modeled as polytopes with Gaussian-distributed faces (PGDFs). A number of practical algorithms exist for motion planning in the presence of known obstacles by constructing a graph in configuration space, then efficiently searching the graph to find a collision-free path. We show that such an exact algorithm is unlikely to be practical in the domain with uncertain obstacles. In particular, we show that safe 2D motion planning among PGDF obstacles is [Formula: see text]-hard with respect to the number of obstacles, and remains [Formula: see text]-hard after being restricted to a graph. Our reduction is based on a path encoding of MAXQHORNSAT and uses the risk of collision with an obstacle to encode variable assignments and literal satisfactions. This implies that, unlike in the known case, planning under uncertainty is hard, even when given a graph containing the solution. We further show by reduction from [Formula: see text]-SAT that both safe 3D motion planning among PGDF obstacles and the related minimum constraint removal problem remain [Formula: see text]-hard even when restricted to cases where each obstacle overlaps with at most a constant number of other obstacles. 

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5. Motion Planning around Obstacles with Convex Optimization

   Tobia Marcucci, Mark Petersen2 ( May 2022 , ArXivorg)

   Trajectory optimization o↵ers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous di↵erential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization prob- lem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B ́ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap round- ing of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time. 

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