Robust Pushing: Exploiting Quasi-static Belief Dynamics and Contact-informed Optimization

TL;DR

This article investigates how the belief over object configurations propagates through quasi-static contact dynamics, and proposes an informed trajectory sampling mechanism for drawing robot trajectories that are likely to make contact with the object.

Abstract

Non-prehensile manipulation such as pushing is typically subject to uncertain, non-smooth dynamics. However, modeling the uncertainty of the dynamics typically results in intractable belief dynamics, making data-efficient planning under uncertainty difficult. This article focuses on the problem of efficiently generating robust open-loop pushing plans. First, we investigate how the belief over object configurations propagates through quasi-static contact dynamics. We exploit the simplified dynamics to predict the variance of the object configuration without sampling from a perturbation distribution. In a sampling-based trajectory optimization algorithm, the gain of the variance is constrained in order to enforce robustness of the plan. Second, we propose an informed trajectory sampling mechanism for drawing robot trajectories that are likely to make contact with the object. This sampling mechanism is shown to significantly improve chances of finding robust solutions, especially when making-and-breaking contacts is required. We demonstrate that the proposed approach is able to synthesize bi-manual pushing trajectories, resulting in successful long-horizon pushing maneuvers without exteroceptive feedback such as vision or tactile feedback. We furthermore deploy the proposed approach in a model-predictive control scheme, demonstrating additional robustness against unmodeled perturbations.

Figures (15)

• Figure 1: Our model-based optimization approach synthesizes bi-manual pushing trajectories by controlling the variance of the object configuration, without explicitly modeling contact modes. We show that the robustness of the pushing trajectories is sufficient to successfully push an object over long horizons. The red cubes on the table and the yellow content of the can act as additional perturbations to the contact dynamics.
• Figure 2: Analogies between active robot localization and robust manipulation. Both can be formulated as a belief space planning problem, where the objective is to decrease the uncertainty of the belief over time. While active localization approaches are based on observation models, robust manipulation exploits favorable contact dynamics to achieve the same goal.
• Figure 3: Belief dynamics through contact in a one-dimensional example. a) Illustration of object samples from the uniformly distributed initial belief (orange). The ground truth object is depicted in non-transparent orange. b) After executing a push from left to right, all samples that were on the left of the push were pushed by the robot. c) The probability mass that was on the left-hand side of the push (light-blue) is now concentrated in a distribution at the contact point according to the perturbation distribution (blue). The probability mass on the right-hand side of the push does not change (blue). d) The variance of the predicted object position is therefore a function of the control action, where a robust control action may decrease the variance over time.
• Figure 4: Block diagram depicting one iteration of BS-VP-STO. The algorithm starts with sampling a population of latent candidate trajectory variables $\bm{\varepsilon}$. These are then decoded into robot trajectories $\bm{q}^r_{0:K}$ using a contact prior. For each candidate trajectory the object belief is rolled-out using the nominal object dynamics. The variance gain together with the mean control cost is then used to compute the fitness of each candidate trajectory. Finally, the distribution of candidate trajectory variables weighted by the fitness is used to update the Gaussian approximation of the probability distribution using CMA-ES. After $M$ iterations, the algorithm returns the best performing candidate trajectory as solution.
• Figure 5: Belief dynamics through contact in a two-dimensional example. The three sub-figures on the right illustrate the predicted belief $b_+$ via samples in orange. All three cases started from the same initial belief $b$ that is depicted in the left-most sub-figure. The visualization of the prediction on the left shows an increase of the variance of the object position as a consequence of pushing with a single contact point ($\gamma > 1$). The second prediction shows a constant variance as a consequence of pushing with a flat contact surface ($\gamma = 1$). The right-most sub-figure shows a decrease of the variance of object position as a consequence of pushing with two contact points ($\gamma < 1$).