We present a novel motion planning algorithm for transferring a liquid body from a source to a target container. Our approach uses a receding-horizon optimization strategy that takes into account fluid constraints and avoids collisions. In order to efficiently handle the high-dimensional configuration space of a liquid body, we use system identification to learn its dynamics characteristics using a neural network. We generate the training dataset using stochastic optimization in a transfer-problem-specific search space. The runtime feedback motion planner is used for real-time planning and we observe high success rate in our simulated 2D and 3D fluid transfer benchmarks.
The extension of conventional motion planning algorithms to the manipulation of non-rigid objects has been addressed in the context of virtual suturing @cite_12 , cloth folding @cite_25 , and surgical simulation @cite_6 . It can be challenging to deal with non-rigid objects with high-dimensional configuration spaces. This is especially the case with liquid manipulation tasks, where the dimension can be as high as several million (see @cite_3 for a detailed discussion). For certain types of fluids such as smoke and fire, optimization-based motion planning can be adapted to solve the problem by exploiting the special structure of the resulting fluid simulator @cite_7 @cite_16 . However, it is non-trivial to extend these methods to control liquid bodies with non-smooth, rapidly-changing free surfaces. Moreover, prior methods are designed for offline applications and computationally very costly. Previous work @cite_10 reduced the computational cost by using a much simplified liquid model, dependent on just two variables.
@cite_7 @cite_3 @cite_6 @cite_16 @cite_10 @cite_25 @cite_12
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We describe a method for controlling smoke simulations through user-specified keyframes. To achieve the desired behavior, a continuous quasi-Newton optimization solves for appropriate "wind" forces to be applied to the underlying velocity field throughout the simulation. The cornerstone of our approach is a method to efficiently compute exact derivatives through the steps of a fluid simulation. We formulate an objective function corresponding to how well a simulation matches the user's keyframes, and use the derivatives to solve for force parameters that minimize this function. For animations with several keyframes, we present a novel multiple-shooting approach. By splitting large problems into smaller overlapping subproblems, we greatly speed up the optimization process while avoiding certain local minima. We present a new algorithm to compute a collision-free trajectory for a robot manipulator to pour liquid from one container to the other. Our formulation uses a physical fluid model to simulate its highly deformable motion. We present a simulation guided and optimization based method to automatically compute the transferring trajectory. We use the full-featured and accurate Navier-Stokes model that provides the fine-grained information of velocity distribution inside the liquid body. Moreover, this information is used as an additional guiding energy term for the planner. Our approach includes a tight integration between the fine-grained fluid simulator, liquid transfer controller, and the optimization-based planner. We have implemented the method using a hybrid particle-mesh fluid simulator (FLIP) and demonstrated its performance on 4 benchmarks with different cup shapes and viscosity coefficients. We present algorithms for simulating and visualizing the insertion and steering of needles through deformable tissues for surgical training and planning. Needle insertion is an essential component of many clinical procedures such as biopsies, injections, neurosurgery, and brachytherapy cancer treatment. The success of these procedures depends on accurate guidance of the needle tip to a clinical target while avoiding vital tissues. Needle insertion deforms body tissues, making accurate placement difficult. Our interactive needle insertion simulator models the coupling between a steerable needle and deformable tissue. We introduce (1) a novel algorithm for local remeshing that quickly enforces the conformity of a tetrahedral mesh to a curvilinear needle path, enabling accurate computation of contact forces, (2) an efficient method for coupling a 3D finite element simulation with a 1D inextensible rod with stick-slip friction, and (3) optimizations that reduce the computation time for physically based simulations. We can realistically and interactively simulate needle insertion into a prostate mesh of 13,375 tetrahedra and 2,763 vertices at a 25 Hz frame rate on an 8-core 3.0 GHz Intel Xeon PC. The simulation models prostate brachytherapy with needles of varying stiffness, steering needles around obstacles, and supports motion planning for robotic needle insertion. We evaluate the accuracy of the simulation by comparing against real-world experiments in which flexible, steerable needles were inserted into gel tissue phantoms. During the last decade, sampling-based path planning algorithms, such as probabilistic roadmaps (PRM) and rapidly exploring random trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g. as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g. showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs. Robotic manipulation of deformable objects remains a challenging task. One such task is folding a garment autonomously. Given start and end folding positions, what is an optimal trajectory to move the robotic arm to fold a garment? Certain trajectories will cause the garment to move, creating wrinkles, and gaps, other trajectories will fail altogether. We present a novel solution to find an optimal trajectory that avoids such problematic scenarios. The trajectory is optimized by minimizing a quadratic objective function in an off-line simulator, which includes material properties of the garment and frictional force on the table. The function measures the dissimilarity between a user folded shape and the folded garment in simulation, which is then used as an error measurement to create an optimal trajectory. We demonstrate that our two-arm robot can follow the optimized trajectories, achieving accurate and efficient manipulations of deformable objects.