arXiv subjects

Maxim Likhachev

Publications and source records attributed to Maxim Likhachev.

77 records · Page 5Linked to original sources

arXiv2019

Effective Footstep Planning Using Homotopy-Class Guidance

Planning the motion for humanoid robots is a computationally-complex task due to the high dimensionality of the system. Thus, a common approach is to first plan in the low-dimensional space induced by the robot's feet---a task referred to as footstep planning. This low-dimensional plan is then used to guide the full motion of the robot. One approach that has proven successful in footstep planning is using search-based planners such as A* and its many variants. To do so, these search-based planners have to be endowed with effective heuristics to efficiently guide them through the search space. However, designing effective heuristics is a time-consuming task that requires the user to have good domain knowledge. Thus, our goal is to be able to effectively plan the footstep motions taken by a humanoid robot while obviating the burden on the user to carefully design local-minima free heuristics. To this end, we propose to use user-defined homotopy classes in the workspace that are intuitive to define. These homotopy classes are used to automatically generate heuristic functions that efficiently guide the footstep planner. Additionally, we present an extension to homotopy classes such that they are applicable to complex multi-level environments. We compare our approach for footstep planning with a standard approach that uses a heuristic common to footstep planning. In simple scenarios, the performance of both algorithms is comparable. However, in more complex scenarios our approach allows for a speedup in planning of several orders of magnitude when compared to the standard approach.

cs.RO↗

arXiv2018

Online, interactive user guidance for high-dimensional, constrained motion planning

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration $\hat{q}$, which is used to bias the planner to go through $\hat{q}$. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafting domain-dependent heuristics.

cs.RO↗

arXiv2018

A Single-Planner Approach to Multi-Modal Humanoid Mobility

In this work, we present an approach to planning for humanoid mobility. Humanoid mobility is a challenging problem, as the configuration space for a humanoid robot is intractably large, especially if the robot is capable of performing many types of locomotion. For example, a humanoid robot may be able to perform such tasks as bipedal walking, crawling, and climbing. Our approach is to plan for all these tasks within a single search process. This allows the search to reason about all the capabilities of the robot at any point, and to derive the complete solution such that the plan is guaranteed to be feasible. A key observation is that we often can roughly decompose a mobility task into a sequence of smaller tasks, and focus planning efforts to reason over much smaller search spaces. To this end, we leverage the results of a recently developed framework for planning with adaptive dimensionality, and incorporate the capabilities of available controllers directly into the planning process. The resulting planner can also be run in an interleaved fashion alongside execution so that time spent idle is much reduced.

cs.RO↗

arXiv2016

PERCH: Perception via Search for Multi-Object Recognition and Localization

In many robotic domains such as flexible automated manufacturing or personal assistance, a fundamental perception task is that of identifying and localizing objects whose 3D models are known. Canonical approaches to this problem include discriminative methods that find correspondences between feature descriptors computed over the model and observed data. While these methods have been employed successfully, they can be unreliable when the feature descriptors fail to capture variations in observed data; a classic cause being occlusion. As a step towards deliberative reasoning, we present PERCH: PErception via SeaRCH, an algorithm that seeks to find the best explanation of the observed sensor data by hypothesizing possible scenes in a generative fashion. Our contributions are: i) formulating the multi-object recognition and localization task as an optimization problem over the space of hypothesized scenes, ii) exploiting structure in the optimization to cast it as a combinatorial search problem on what we call the Monotone Scene Generation Tree, and iii) leveraging parallelization and recent advances in multi-heuristic search in making combinatorial search tractable. We prove that our system can guaranteedly produce the best explanation of the scene under the chosen cost function, and validate our claims on real world RGB-D test data. Our experimental results show that we can identify and localize objects under heavy occlusion--cases where state-of-the-art methods struggle.

cs.CV↗

arXiv2011

A Homotopy-like Class Invariant for Sub-manifolds of Punctured Euclidean Spaces

We consider the $D$-dimensional Euclidean space, $\mathbb{R}^D$, with certain $(D-N)$-dimensional compact, closed and orientable sub-manifolds (which we call \emph{singularity manifolds} and represent by $\widetilde{\mathcal{S}}$) removed from it. We define and investigate the problem of finding a homotopy-like class invariant ($χ$-homotopy) for certain $(N-1)$-dimensional compact, closed and orientable sub-manifolds (which we call \emph{candidate manifolds} and represent by $ω$) of $\mathbb{R}^D \setminus \widetilde{\mathcal{S}}$, with special emphasis on computational aspects of the problem. We determine a differential $(N-1)$-form, $ψ_{\widetilde{\mathcal{S}}}$, such that $χ_{\widetilde{\mathcal{S}}}(ω) = \int_ωψ_{\widetilde{\mathcal{S}}}$ is a class invariant for such candidate manifolds. We show that the formula agrees with formulae from Cauchy integral theorem and Residue theorem of complex analysis (when $D=2,N=2$), Biot-Savart law and Ampere's law of theory of electromagnetism (when $D=3,N=2$), and the Gauss divergence theorem (when $D=3,N=3$), and discover that the underlying equivalence relation suggested by each of these well-known theorems is the $χ$-homotopy of sub-manifolds of these low dimensional punctured Euclidean spaces. We describe numerical techniques for computing $ψ_{\widetilde{\mathcal{S}}}$ and its integral on $ω$, and give numerical validations of the proposed theory for a problem in a 5-dimensional Euclidean space. We also discuss a specific application from \emph{robot path planning problem}, when N=2, and describe a method for computing least cost paths with homotopy class constraints using \emph{graph search techniques}.

math.DG↗