Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot’s geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: https://sites.google.com/view/alspg-oc

Control of dynamic systems involving hybrid actions is a challenging task in robotics. To address this, we present a novel algorithm called Generalized Policy Iteration using Tensor Train (TTPI) that belongs to the class of Approximate Dynamic Programming (ADP). We use a low-rank tensor approximation technique called Tensor Train (TT) to approximate the state-value and advantage function which enables us to efficiently handle hybrid systems. We demonstrate the superiority of our approach over previous baselines for some benchmark problems with hybrid action spaces. Additionally, the robustness and generalization of the policy for hybrid systems are showcased through a real-world robotics experiment involving a non-prehensile manipulation task which is considered to be a highly challenging control problem.

Many real-world sequential manipulation tasks involve a combination of discrete symbolic search and continuous motion planning, collectively known as combined task and motion planning (TAMP). However, prevailing methods often struggle with the computational burden and intricate combinatorial challenges, limiting their applications for online replanning in the real world. To address this, we propose Dynamic Logic-Geometric Program (D-LGP), a novel approach integrating Dynamic Tree Search and global optimization for efficient hybrid planning. Through empirical evaluation on three benchmarks, we demonstrate the efficacy of our approach, showcasing superior performance in comparison to state-of-the-art techniques. We validate our approach through simulation and demonstrate its reactive capability to cope with online uncertainty and external disturbances in the real world. Project webpage: https://sites.google.com/view/dyn-lgp.

Robot in-hand manipulation is an important skill for robots to carry out sophisticated tasks that require moving the grasped object within hand. In this work, we present the Roller Grasper V3, a nonanthropomorphic robot grasper with a steerable roller on each of its four fingertips, and a manipulation architecture that enables the Roller Grasper V3 to achieve full 6-DoF manipulation of the grasped object in$SE(3)$. The manipulation architecture consists of a high-level planner that searches for a feasible path with waypoints for the object to be manipulated, and a low-level control policy that is used to navigate the object in between the adjacent waypoints. The method was experimentally validated on the Roller Grasper V3 to manipulate multiple objects with different geometries and topologies.

Long-term non-prehensile planar manipulation is a challenging task for robot planning and feedback control. It is characterized by underactuation, hybrid control, and contact uncertainty. One main difficulty is to determine both the continuous and discrete contact configurations, e.g., contact points and modes, which requires joint logical and geometrical reasoning. To tackle this issue, we propose a demonstration-guided hierarchical optimization framework to achieve offline task and motion planning (TAMP). Our work extends the formulation of the dynamics model of the pusher-slider system to include separation mode with face switching mechanism, and solves a warm-started TAMP problem by exploiting human demonstrations. We show that our approach can cope well with the local minima problems currently present in the state-of-the-art solvers and determine a valid solution to the task. We validate our results in simulation and demonstrate its applicability on a pusher-slider system with a real Franka Emika robot in the presence of external disturbances. Project webpage: https://sites.google.com/view/dg-oc/.