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.

Safety in the face of uncertainty is a key challenge in robotics. We introduce a real-time capable framework to generate safe and task-efficient robot motions for stochastic control problems. We frame this as a chance-constrained optimisation problem constraining the probability of the controlled system to violate a safety constraint to be below a set threshold. To estimate this probability we propose a Monte--Carlo approximation. We suggest several ways to construct the problem given a fixed number of uncertainty samples, such that it is a reliable over-approximation of the original problem, i.e. any solution to the sample-based problem adheres to the original chance-constraint with high confidence. To solve the resulting problem, we integrate it into our motion planner VP-STO and name the enhanced framework Chance-Constrained (CC)-VPSTO. The strengths of our approach lie in i) its generality, without assumptions on the underlying uncertainty distribution, system dynamics, cost function, or the form of inequality constraints; and ii) its applicability to MPC-settings. We demonstrate the validity and efficiency of our approach on both simulation and real-world robot experiments.

Abstract-- Achieving reactive robot behavior in complex dynamic environments is still challenging as it relies on being able to solve trajectory optimization problems quickly enough, such that we can replan the future motion at frequencies which are sufficiently high for the task at hand. We argue that current limitations in Model Predictive Control (MPC) for robot manipulators arise from inefficient, high-dimensional trajectory representations and the negligence of time-optimality in the trajectory optimization process. Therefore, we propose a motion optimization framework that optimizes jointly over space and time, generating smooth and timing-optimal robot trajectories in joint-space. Such task settings require performance. Compared to gradient-based optimization, the robot to be reactive to unforeseen changes in stochastic approaches typically also achieve higher robustness the environment, e.g., due to dynamic obstacles, as well to difficult reward landscapes due to their exploratory as to be robust and compliant when operating alongside properties [5].