In order to enable microaerial vehicles (MAVs) to assist in complex, unknown, unstructured environments, they must be able to navigate with guaranteed safety, even when faced with a cluttered environment they have no prior knowledge of. While trajectory-optimization-based local planners have been shown to perform well in these cases, prior work either does not address how to deal with local minima in the optimization problem or solves it by using an optimistic global planner. We present a conservative trajectory-optimization-based local planner, coupled with a local exploration strategy that selects intermediate goals. We perform extensive simulations to show that this system performs better than the standard approach of using an optimistic global planner and also outperforms doing a single exploration step when the local planner is stuck. The method is validated through experiments in a variety of highly cluttered environments including a dense forest. These experiments show the complete system running in real time fully onboard an MAV, mapping and replanning at 4 Hz.
Pivtoraiko al use graph search with motion primitives to replan online @cite_1 . However, they use an optimistic local planner: unknown space is considered traversible, and while this helps escape local minima, it is fundamentally unsafe. Chen al plan online by building a sparse graph by inflating unoccupied corridors within an Octomap, then optimize an unconstrained QP to get a polynomial path @cite_24 . However, they only use 2D sensing and treat unknown space as free, again leading to potentially unsafe paths in very cluttered environments.
@cite_24 @cite_1
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We would like robots to be able to safely navigate at high speed, efficiently use local 3D information, and robustly plan motions that consider pose uncertainty of measurements in a local map structure. This is hard to do with previously existing mapping approaches, like occupancy grids, that are focused on incrementally fusing 3D data into a common world frame. In particular, both their fragile sensitivity to state estimation errors and computational cost can be limiting. We develop an alternative framework, NanoMap, which alleviates the need for global map fusion and enables a motion planner to efficiently query pose-uncertainty-aware local 3D geometric information. The key idea of NanoMap is to store a history of noisy relative pose transforms and search over a corresponding set of depth sensor measurements for the minimum-uncertainty view of a queried point in space. This approach affords a variety of capabilities not offered by traditional mapping techniques: (a) the pose uncertainty associated with 3D data can be incorporated in motion planning, (b) poses can be updated (i.e., from loop closures) with minimal computational effort, and (c) 3D data can be fused lazily for the purpose of planning. We provide an open-source implementation of NanoMap, and analyze its capabilities and computational efficiency in simulation experiments. Finally, we demonstrate in hardware its effectiveness for fast 3D obstacle avoidance onboard a quadrotor flying up to 10 m s. We propose a humanoid robot navigation planning framework that reuses previous experience to decrease planning time. The framework is intended for navigating complex unstructured environments using both palm and foot contacts. In a complex environment, discrete-search-based contact space planners trade-off between high branching factor and action flexibility. Although approaches such as weighted A∗, ARA∗ and ANA∗ could speed up the search by compromising on optimality, they can be very slow when the heuristic is inaccurate. In the proposed framework, an experience-retrieval module is added in parallel to ANA∗. This module collects previously-generated motion plans and clusters them based on contact pose similarity to form a motion plan library. To retrieve an appropriate plan from the library for a given environment, the framework uses a distance between the contact poses in the plan and environment surfaces. Candidate plans are then modified with local trajectory optimization until a plan fitting the query environment is found. Our experiments show that the proposed framework outperforms planning-from-scratch in success rate in unstructured environments by at least 28 and can navigate difficult environments such as rubble and narrow corridors. We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density ϕ, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to explicitly compute, the quantity ϕ subject to uniqueness of a relevant Gibbs measure for the factor model on T. By way of example we compute ϕ for the independent set (or hard-core) model at low fugacity, for the ferromagnetic Ising model at all parameter values, and for the ferromagnetic Potts model with both weak enough and strong enough interactions. Even beyond uniqueness regimes our interpolation provides useful explicit bounds on ϕ. In the regimes in which we establish existence of the limit, we show that it coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation (Bethe) recursions on T. In the special case that T has a Galton–Watson law, this formula coincides with the nonrigorous “Bethe prediction” obtained by statistical physicists using the “replica” or “cavity” methods. Thus our work is a rigorous generalization of these heuristic calculations to the broader class of sparse graph sequences converging locally to trees. We also provide a variational characterization for the Bethe prediction in this general setting, which is of independent interest. This paper studies the problem of recovering a sparse signal x ∈ ℝn from highly corrupted linear measurements y = Ax + e ∈ ℝm, where e is an unknown error vector whose nonzero entries may be unbounded. Motivated by an observation from face recognition in computer vision, this paper proves that for highly correlated (and possibly overcomplete) dictionaries A, any sufficiently sparse signal x can be recovered by solving an l1 -minimization problem min ||x||1 + ||e||1 subject to y = Ax + e. More precisely, if the fraction of the support of the error e is bounded away from one and the support of a: is a very small fraction of the dimension m, then as m becomes large the above l1 -minimization succeeds for all signals x and almost all sign-and-support patterns of e. This result suggests that accurate recovery of sparse signals is possible and computationally feasible even with nearly 100 of the observations corrupted. The proof relies on a careful characterization of the faces of a convex polytope spanned together by the standard crosspolytope and a set of independent identically distributed (i.i.d.) Gaussian vectors with nonzero mean and small variance, dubbed the "cross-and-bouquet" (CAB) model. Simulations and experiments corroborate the findings, and suggest extensions to the result.