This work addresses the problem of coupling vision-based navigation systems for Unmanned Aerial Vehicles (UAVs) with robust obstacle avoidance capabilities. The former is formulated by a maximization of the point of interest visibility, while the latter is modeled by ellipsoidal repulsive areas. The whole problem is transcribed into an Optimal Control Problem (OCP), and solved in a few milliseconds by leveraging state-of-the-art numerical optimization. The resulting trajectories are then well suited to achieve the specified goal location while avoiding obstacles by a safety margin and minimizing the probability to loose track with the target of interest. Combining this technique with a proper ellipsoid shaping (e.g. augmenting the shape with the obstacle velocity, or the obstacle detection uncertainties) results in a robust obstacle avoidance behaviour. We validate our approach within extensive simulated experiments demonstrating (i) capability to satisfy all the constraints, and (ii) the avoidance reactivity even in challenging situations. We release with this paper the open source implementation
The collision-free trajectory generation (requirement 2) is usually categorized into three main strategies: search-based approaches @cite_20 @cite_23 , optimization-based approaches @cite_1 @cite_25 , path sampling and motion primitives @cite_4 @cite_6 .
@cite_4 @cite_1 @cite_6 @cite_23 @cite_25 @cite_20
1986417217 2014776084 2293883387 2163913482
This paper presents a method for optimal trajectory generation for discrete-time nonlinear systems with linear temporal logic (LTL) task specifications. Our approach is based on recent advances in stochastic optimization algorithms for optimal trajectory generation. These methods rely on estimation of the rare event of sampling optimal trajectories, which is achieved by incrementally improving a sampling distribution so as to minimize the cross-entropy. A key component of these stochastic optimization algorithms is determining whether or not a trajectory is collision-free. We generalize this collision checking to efficiently verify whether or not a trajectory satisfies a LTL formula. Interestingly, this verification can be done in time polynomial in the length of the LTL formula and the trajectory. We also propose a method for efficiently re-using parts of trajectories that only partially satisfy the specification, instead of simply discarding the entire sample. Our approach is demonstrated through numerical experiments involving Dubins car and a generic point-mass model subject to complex temporal logic task specifications. We designed a distributed collision-free formation flight control law in the framework of nonlinear model predictive control. Formation configuration is determined in the virtual reference point coordinate system. Obstacle avoidance is guaranteed by cost penalty, and intervehicle collision avoidance is guaranteed by cost penalty combined with a new priority strategy. 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. The paper presents an efficient collision-free path planner for mechanical part disassembly simulation. The principle of the algorithm involves computing a first path while allowing some penetration within the obstacles. Then the current paths are iteratively re-shaped by decreasing the allowed penetration threshold. The process is controlled by a dynamic collision checker. The cases of failure of the iterative process are automatically detected and solved.