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Register a new userIncrementally Stochastic and Accelerated Gradient Information mixed Optimization for Manipulator Motion Planning
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Added by
Yichang Feng
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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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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.
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.
Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robots torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion generality while keeping a low computation time.
Sampling-based motion planners rely on incremental densification to discover progressively shorter paths. After computing feasible path $xi$ between start $x_s$ and goal $x_t$, the Informed Set (IS) prunes the configuration space $mathcal{C}$ by conservatively eliminating points that cannot yield shorter paths. Densification via sampling from this Informed Set retains asymptotic optimality of sampling from the entire configuration space. For path length $c(xi)$ and Euclidean heuristic $h$, $IS = { x | x in mathcal{C}, h(x_s, x) + h(x, x_t) leq c(xi) }$. Relying on the heuristic can render the IS especially conservative in high dimensions or complex environments. Furthermore, the IS only shrinks when shorter paths are discovered. Thus, the computational effort from each iteration of densification and planning is wasted if it fails to yield a shorter path, despite improving the cost-to-come for vertices in the search tree. Our key insight is that even in such a failure, shorter paths to vertices in the search tree (rather than just the goal) can immediately improve the planners sampling strategy. Guided Incremental Local Densification (GuILD) leverages this information to sample from Local Subsets of the IS. We show that GuILD significantly outperforms uniform sampling of the Informed Set in simulated $mathbb{R}^2$, $SE(2)$ environments and manipulation tasks in $mathbb{R}^7$.
For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex optimization problem. We devise a new algorithm to solve this type of non-convex problems by formulating a rapidly-exploring random tree of barrier pairs, with each barrier pair composed of a quadratic barrier function and a full state feedback controller. The proposed method employs a rapid-exploring random tree to deal with the non-convex constraints and uses barrier pairs to fulfill the local convex constraints. As such, the method solves control problems fulfilling the required transitions of an automaton in order to satisfy given linear temporal logic constraints. At the same time it synthesizes locally optimal controllers in order to transition between the regions corresponding to the alphabet of the automaton. We demonstrate this new algorithm on a simulation of a two linkage manipulator robot.
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