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Register a new userPath Homotopy Invariants and their Application to Optimal Trajectory Planning
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Added by
Subhrajit Bhattacharya
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on subsets of the Euclidean plane in the robotics literature. The problem of finding optimal trajectories in different homotopy classes in more general configuration spaces (or even characterizing the homotopy classes of such trajectories) can be difficult. In this paper we propose automated solutions to this problem in several general classes of configuration spaces by constructing presentations of fundamental groups and giving algorithms for solving the emph{word problem} in such groups. We present explicit results that apply to knot and link complements in 3-space, discuss how to extend to cylindrically-deleted coordination spaces of arbitrary dimension, and also present results in the coordination space of robots navigating on an Euclidean plane.
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The problem of constrained coverage path planning involves a robot trying to cover maximum area of an environment under some constraints that appear as obstacles in the map. Out of the several coverage path planning methods, we consider augmenting the linear sweep-based coverage method to achieve minimum energy/ time optimality along with maximum area coverage. In addition, we also study the effects of variation of different parameters on the performance of the modified method.
In this paper, a novel real-time acceleration-continuous path-constrained trajectory planning algorithm is proposed with an appealing built-in tradability mechanism between cruise motion and time-optimal motion. Different from existing approaches, the proposed approach smoothens time-optimal trajectories with bang-bang input structures to generate acceleration-continuous trajectories while preserving the completeness property. More importantly, a novel built-in tradability mechanism is proposed and embedded into the trajectory planning framework, so that the proportion of the cruise motion and time-optimal motion can be flexibly adjusted by changing a user-specified functional parameter. Thus, the user can easily apply the trajectory planning algorithm for various tasks with different requirements on motion efficiency and cruise proportion. Moreover, it is shown that feasible trajectories are computed more quickly than optimal trajectories. Rigorous mathematical analysis and proofs are provided for these aforementioned results. Comparative simulation and experimental results on omnidirectional wheeled mobile robots demonstrate the capability of the proposed algorithm in terms of flexible tunning between cruise and time-optimal motions, as well as higher computational efficiency.
It is ubiquitously accepted that during the autonomous navigation of the quadrotors, one of the most widely adopted unmanned aerial vehicles (UAVs), safety always has the highest priority. However, it is observed that the ego airflow disturbance can be a significant adverse factor during flights, causing potential safety issues, especially in narrow and confined indoor environments. Therefore, we propose a novel method to estimate and adapt indoor ego airflow disturbance of quadrotors, meanwhile applying it to trajectory planning. Firstly, the hover experiments for different quadrotors are conducted against the proximity effects. Then with the collected acceleration variance, the disturbances are modeled for the quadrotors according to the proposed formulation. The disturbance model is also verified under hover conditions in different reconstructed complex environments. Furthermore, the approximation of Hamilton-Jacobi reachability analysis is performed according to the estimated disturbances to facilitate the safe trajectory planning, which consists of kinodynamic path search as well as B-spline trajectory optimization. The whole planning framework is validated on multiple quadrotor platforms in different indoor environments.
Rapidly-exploring Random Tree Star(RRT*) is a recently proposed extension of Rapidly-exploring Random Tree (RRT) algorithm that provides a collision-free, asymptotically optimal path regardless of obstacles geometry in a given environment. However, one of the limitations in the RRT* algorithm is slow convergence to optimal path solution. As a result, it consumes high memory as well as time due to a large number of iterations utilised in achieving optimal path solution. To overcome these limitations, we propose the Potential Function Based-RRT* (P-RRT*) that incorporates the Artificial Potential Field Algorithm in RRT*. The proposed algorithm allows a considerable decrease in the number of iterations and thus leads to more efficient memory utilization and an accelerated convergence rate. In order to illustrate the usefulness of the proposed algorithm in terms of space execution and convergence rate, this paper presents rigorous simulation based comparisons between the proposed techniques and RRT* under different environmental conditions. Moreover, both algorithms are also tested and compared under non-holonomic differential constraints.
With the development of human space exploration, the space environment is gradually filled with abandoned satellite debris and unknown micrometeorites, which will seriously affect capture motion of space robot. Hence, a novel fast collision-avoidance trajectory planning strategy for a dual-arm free-floating space robot (FFSR) with predefined-time pose feedback will be mainly studied to achieve micron-level tracking accuracy of end-effector in this paper. However, similar to control, the exponential feedback results in larger initial joint angular velocity relative to proportional feedback. Firstly, a pose-error-based kinematic model of the FFSR will be derived from a control perspective. Then, a cumulative dangerous field (CDF) collision-avoidance algorithm is applied in predefined-time trajectory planning to achieve micron-level collision-avoidance trajectory tracking precision. In the end, a GA-based optimization algorithm is used to optimize the predefined-time parameter to obtain a motion trajectory of low joint angular velocity of robotic arms. The simulation results verify our conjecture and conclusion.
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