We address prehensile pushing, the problem of manipulating a grasped object by pushing against the environment. Our solution is an efficient nonlinear trajectory optimization problem relaxed from an exact mixed integer non-linear trajectory optimization formulation. The critical insight is recasting the external pushers (environment) as a discrete probability distribution instead of binary variables and minimizing the entropy of the distribution. The probabilistic reformulation allows all pushers to be used simultaneously, but at the optimum, the probability mass concentrates onto one due to the entropy minimization. We numerically compare our method against a state-of-the-art sampling-based baseline on a prehensile pushing task. The results demonstrate that our method finds trajectories 8 times faster and at a 20 times lower cost than the baseline. Finally, we demonstrate that a simulated and real Franka Panda robot can successfully manipulate different objects following the trajectories proposed by our method. Supplementary materials are available at https://probabilistic-prehensile-pushing.github.io/.

Thus, it is We can make very skillful use of various contacts desirable that a planning algorithm be robust to various (e.g., with the environment, our own body, etc.) to perform uncertainties like grasp center, extrinsic contact location, etc. complex manipulation. In a striking contrast, achieving such We present a method which can incorporate uncertainties in dexterous behavior for robots remains very challenging. Using several of the kinematic constraints to generate robust plans environmental contacts efficiently can provide additional for perform in-hand manipulation. This idea is also illustrated dexterity to robots while performing complex manipulation in Figure 1, where a naïve plan can easily lose contact with the [1]. However, the current generation of robotic systems environment due to uncertainty in the grasp location or the mostly avoid making contacts with their environment.

This paper addresses the problem of pushing manipulation with nonholonomic mobile robots. Pushing is a fundamental skill that enables robots to move unwieldy objects that cannot be grasped. We propose a stable pushing method that maintains stiff contact between the robot and the object to avoid consuming repositioning actions. We prove that a line contact, rather than a single point contact, is necessary for nonholonomic robots to achieve stable pushing. We also show that the stable pushing constraint and the nonholonomic constraint of the robot can be simplified as a concise linear motion constraint. Then the pushing planning problem can be formulated as a constrained optimization problem using nonlinear model predictive control (NMPC). According to the experiments, our NMPC-based planner outperforms a reactive pushing strategy in terms of efficiency, reducing the robot's traveled distance by 23.8\% and time by 77.4\%. Furthermore, our method requires four fewer hyperparameters and decision variables than the Linear Time-Varying (LTV) MPC approach, making it easier to implement. Real-world experiments are carried out to validate the proposed method with two differential-drive robots, Husky and Boxer, under different friction conditions.