In this paper, we propose a time-efficient approach to generate safe, smooth and dynamically feasible trajectories for quadrotors in obstacle-cluttered environment. By using the uniform B-spline to represent trajectories, we transform the trajectory planning to a graph-search problem of B-spline control points in discretized space. Highly strict convex hull property of B-spline is derived to guarantee the dynamical feasibility of the entire trajectory. A novel non-uniform kinodynamic search strategy is adopted, and the step length is dynamically adjusted during the search process according to the Euclidean signed distance field (ESDF), making the trajectory achieve reasonable time-allocation and be away from obstacles. Non-static initial and goal states are allowed, therefore it can be used for online local replanning as well as global planning. Extensive simulation and hardware experiments show that our method achieves higher performance comparing with the state-of-the-art method.
Many existing planning methods take a two-step pipeline, i.e. a collision-free path is planned at first, then the smoothness and time-allocation of the relevant trajectory are optimized based on the shape of the path. At the front-end, sampling-based @cite_16 and searching-based @cite_4 @cite_8 methods are used to plan a collision-free path. In the back-end, gradient-based methods @cite_15 and several other methods @cite_1 @cite_12 @cite_3 are employed to guarantee the smoothness and dynamical feasibility. However, these methods separates the trajectory shape and trajectory parameterization, are susceptible to some problems. For example, global optimal trajectory or even feasible trajectory may not be inside the homology class of path which is generated by the front-end methods without dynamic consideration.
@cite_4 @cite_8 @cite_1 @cite_3 @cite_15 @cite_16 @cite_12
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We present an approach to path planning for humanoid robots that computes dynamically-stable, collision-free trajectories from full-body posture goals. Given a geometric model of the environment and a statically-stable desired posture, we search the configuration space of the robot for a collision-free path that simultaneously satisfies dynamic balance constraints. We adapt existing randomized path planning techniques by imposing balance constraints on incremental search motions in order to maintain the overall dynamic stability of the final path. A dynamics filtering function that constrains the ZMP (zero moment point) trajectory is used as a post-processing step to transform statically-stable, collision-free paths into dynamically-stable, collision-free trajectories for the entire body. Although we have focused our experiments on biped robots with a humanoid shape, the method generally applies to any robot subject to balance constraints (legged or not). The algorithm is presented along with computed examples using both simulated and real humanoid robots. We present an optimization-based motion planning algorithm to compute a smooth, collision-free trajectory for a manipulator used to transfer a liquid from a source to a target container. We take into account fluid dynamics constraints as part of the trajectory computation. In order to avoid the high complexity of exact fluid simulation, we introduce a simplified dynamics model based on physically inspired approximations and system identification. Our optimization approach can incorporate various other constraints such as collision avoidance with obstacles, kinematic and dynamics constraints of the manipulator, and fluid dynamics characteristics. We demonstrate the performance of our planner on different benchmarks corresponding to various obstacles and container shapes. We also evaluate its accuracy by validating the motion plan using an accurate but computationally costly Navier-Stokes fluid simulation. In this paper, a new method is presented for motion planning in dynamic environments, that is, finding a trajectory for a robot in a scene consisting of both static and dynamic, moving obstacles. We propose a practical algorithm based on a roadmap that is created for the static part of the scene. On this roadmap, an approximately time-optimal trajectory from a start to a goal configuration is computed, such that the robot does not collide with any moving obstacle. The trajectory is found by performing a two-level search for a shortest path. On the local level, trajectories on single edges of the roadmap are found using a depth-first search on an implicit grid in state-time space. On the global level, these local trajectories are coordinated using an A sup * -search to find a global trajectory to the goal configuration. The approach is applicable to any robot type in configuration spaces with any dimension, and the motions of the dynamic obstacles are unconstrained, as long as they are known beforehand. The approach has been implemented for both free-flying and articulated robots in three-dimensional workspaces, and it has been applied to multirobot motion planning, as well. Experiments show that the method achieves interactive performance in complex environments. We present a novel approach for incorporating collision avoidance into trajectory optimization as a method of solving robotic motion planning problems. At the core of our approach are (i) A sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary. (ii) An efficient formulation of the no-collisions constraint that directly considers continuous-time safety and enables the algorithm to reliably solve motion planning problems, including problems involving thin and complex obstacles. We benchmarked our algorithm against several other motion planning algorithms, solving a suite of 7-degree-of-freedom (DOF) arm-planning problems and 18-DOF full-body planning problems. We compared against sampling-based planners from OMPL, and we also compared to CHOMP, a leading approach for trajectory optimization. Our algorithm was faster than the alternatives, solved more problems, and yielded higher quality paths. Experimental evaluation on the following additional problem types also confirmed the speed and effectiveness of our approach: (i) Planning foot placements with 34 degrees of freedom (28 joints + 6 DOF pose) of the Atlas humanoid robot as it maintains static stability and has to negotiate environmental constraints. (ii) Industrial box picking. (iii) Real-world motion planning for the PR2 that requires considering all degrees of freedom at the same time.