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.
There is considerable work on feedback motion planning that uses refinement schemes based on feedback control laws. This can be performed using replanning @cite_4 @cite_30 @cite_21 or by formulating the problem as a Markov Decision Process @cite_22 . These ideas have been applied to high dimensional continuous systems such as humanoid robots @cite_19 @cite_32 . In this work, we present such a feedback motion planning algorithm for liquid transfer.
@cite_30 @cite_4 @cite_22 @cite_21 @cite_32 @cite_19
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We present a motion planning approach for per- forming a learned task while avoiding obstacles and reacting to the movement of task-relevant objects. We employ a closed-loop sampling-based motion planner that acquires new sensor infor- mation, generates new collision-free plans that are based on a learned task model, and replans at an average rate of more than 10 times per second for a 7-DOF manipulator. The task model is learned from expert demonstrations prior to task execution and is represented as a hidden Markov model. During task execution, our motion planner quickly searches in the Cartesian product of the task model and a probabilistic roadmap for a plan with features most similar to the demonstrations given the locations of the task-relevant objects. We improve the replan rate by using a fast bidirectional search and by biasing the sampling distribution using information from the learned task model to construct high-quality roadmaps. We illustrate the efficacy of our approach by performing a simulated navigation task with a 2D point robot and a physical powder transfer task with the Baxter robot. With the increased use of high degree-of-freedom robots that must perform tasks in real-time, there is a need for fast algorithms for motion planning. In this work, we view motion planning from a probabilistic perspective. We consider smooth continuous-time trajectories as samples from a Gaussian process (GP) and formulate the planning problem as probabilistic inference. We use factor graphs and numerical optimization to perform inference quickly, and we show how GP interpolation can further increase the speed of the algorithm. Our framework also allows us to incrementally update the solution of the planning problem to contend with changing conditions. We benchmark our algorithm against several recent trajectory optimization algorithms on planning problems in multiple environments. Our evaluation reveals that our approach is several times faster than previous algorithms while retaining robustness. Finally, we demonstrate the incremental version of our algorithm on replanning problems, and show that it often can find successful solutions in a fraction of the time required to replan from scratch. Replanning is a powerful mechanism for controlling robot motion under hard constraints and unpredictable disturbances, but it involves an inherent tradeoff between the planner's power (e.g., a planning horizon or time cutoff) and its responsiveness to disturbances. This paper presents an adaptive time-stepping architecture for real-time planning with several advantageous properties. By dynamically adapting to the amount of time needed for a sample-based motion planner to make progress toward the goal, the technique is robust to the typically high variance exhibited by replanning queries. The technique is proven to be safe and asymptotically complete in a deterministic environment and a static objective. For unpredictably moving obstacles, the technique can be applied to keep the robot safe more reliably than reactive obstacle avoidance or fixed time-step replanning. It can also be applied in a contingency planning algorithm that achieves simultaneous safety-seeking and goal-seeking motion. These techniques generate responsive and safe motion in both simulated and real robots across a range of difficulties, including applications to bounded-acceleration pursuit-evasion, indoor navigation among moving obstacles, and aggressive collision-free teleoperation of an industrial robot arm. As sampling-based motion planners become faster, they can be reexecuted more frequently by a robot during task execution to react to uncertainty in robot motion, obstacle motion, sensing noise, and uncertainty in the robot's kinematic model. We investigate and analyze high-frequency replanning (HFR) where, during each period, fast sampling-based motion planners are executed in parallel as the robot simultaneously executes the first action of the best motion plan from the previous period. We consider discrete-time systems with stochastic nonlinear (but linearizable) dynamics and observation models with noise drawn from zero mean Gaussian distributions. The objective is to maximize the probability of success (i.e., avoid collision with obstacles and reach the goal) or to minimize path length subject to a lower bound on the probability of success. We show that, as parallel computation power increases, HFR offers asymptotic optimality for these objectives during each period for goal-oriented problems. We then demonstrate the effectiveness of HFR for holonomic and nonholonomic robots including car-like vehicles and steerable medical needles.