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Register a new userApproximate Topological Optimization using Multi-Mode Estimation for Robot Motion Planning
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Added by
Andreas Orthey
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path optimization problem. This is important to compress path databases, as contingencies for replanning and as source of symbolic representations. Following ideas from Morse theory, we define modes as paths invariant under optimization of a cost functional. We develop a multi-mode estimation algorithm which approximately finds all modes of a given motion optimization problem and asymptotically converges. This is made possible by integrating sparse roadmaps with an existing single-mode optimization algorithm. Initial evaluation results show the multi-mode estimation algorithm as a promising direction to study path spaces from a topological point of view.
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Motion planning for multi-jointed robots is challenging. Due to the inherent complexity of the problem, most existing works decompose motion planning as easier subproblems. However, because of the inconsistent performance metrics, only sub-optimal solution can be found by decomposition based approaches. This paper presents an optimal control based approach to address the path planning and trajectory planning subproblems simultaneously. Unlike similar works which either ignore robot dynamics or require long computation time, an efficient numerical method for trajectory optimization is presented in this paper for motion planning involving complicated robot dynamics. The efficiency and effectiveness of the proposed approach is shown by numerical results. Experimental results are used to show the feasibility of the presented planning algorithm.
In this paper, we present a motion planning framework for multi-modal vehicle dynamics. Our proposed algorithm employs transcription of the optimization objective function, vehicle dynamics, and state and control constraints into sparse factor graphs, which -- combined with mode transition constraints -- constitute a composite pose graph. By formulating the multi-modal motion planning problem in composite pose graph form, we enable utilization of efficient techniques for optimization on sparse graphs, such as those widely applied in dual estimation problems, e.g., simultaneous localization and mapping (SLAM). The resulting motion planning algorithm optimizes the multi-modal trajectory, including the location of mode transitions, and is guided by the pose graph optimization process to eliminate unnecessary transitions, enabling efficient discovery of optimized mode sequences from rough initial guesses. We demonstrate multi-modal trajectory optimization in both simulation and real-world experiments for vehicles with various dynamics models, such as an airplane with taxi and flight modes, and a vertical take-off and landing (VTOL) fixed-wing aircraft that transitions between hover and horizontal flight modes.
This paper considers the problem of multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot optimal control policy is challenging not only because of the complexity of incorporating dynamic uncertainties while planning, but also because of the exponential growth in problem size as a function of number of robots. Leveraging recent works obtaining a tractable safety maximizing plan for a single robot, we propose a scalable two-stage framework to solve the problem at hand. Specifically, the problem is split into a low-level single-agent planning problem and a high-level task allocation problem. The low-level problem uses an efficient approximation of stochastic reachability for a Markov decision process to handle the dynamic uncertainty. The task allocation, on the other hand, is solved using polynomial-time forward and reverse greedy heuristics. The multiplicative safety objective of our multi-robot safe planning problem allows decoupling in order to implement the greedy heuristics through a distributed auction-based approach. Moreover, by leveraging the properties of this safety objective function, we ensure provable performance bounds on the safety of the approximate solutions proposed by these two heuristics.
This paper introduces a novel motion planning algorithm, incrementally stochastic and accelerated gradient information mixed optimization (iSAGO), for robotic manipulators in a narrow workspace. Primarily, we propose the overall scheme of iSAGO integrating the accelerated and stochastic gradient information for efficient descent in the penalty method. In the stochastic part, we generate the adaptive stochastic moment via the random selection of collision checkboxes, interval time-series, and penalty factor based on Adam to solve the body-obstacle stuck case. Due to the slow convergence of STOMA, we integrate the accelerated gradient and stimulate the descent rate in a Lipschitz constant reestimation framework. Moreover, we introduce the Bayesian tree inference (BTI) method, transforming the whole trajectory optimization (SAGO) into an incremental sub-trajectory optimization (iSAGO) to improve the computational efficiency and success rate. Finally, we demonstrate the key coefficient tuning, benchmark iSAGO against other planners (CHOMP, GPMP2, TrajOpt, STOMP, and RRT-Connect), and implement iSAGO on AUBO-i5 in a storage shelf. The result shows the highest success rate and moderate solving efficiency of iSAGO.
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