In this article, we present a multi-robot task and motion planning method that, when applied to the rearrangement of objects by manipulators, results in solution times up to three orders of magnitude faster than the existing methods and successfully plans for problems with up to 20 objects, more than three times as many objects as comparable methods. We achieve this improvement by decomposing the planning space to consider manipulators alone, objects, and manipulators holding objects. We represent this decomposition with a hypergraph where vertices are decomposed elements of the planning spaces and hyperarcs are transitions between elements. The existing methods use graph-based representations where vertices are full composite spaces and edges are transitions between these. Using the hypergraph reduces the representation size of the planning space for multimanipulator object rearrangement, the number of hypergraph vertices scales linearly with the number of either robots or objects, while the number of hyperarcs scales quadratically with the number of robots and linearly with the number of objects. In contrast, the number of vertices and edges in graph-based representations scales exponentially in the number of robots and objects. We show that similar gains can be achieved for other multi-robot task and motion planning problems.

Model Predictive Control (MPC) and Reinforcement Learning (RL) are two prominent strategies for controlling legged robots. RL learns control policies through system interaction, adapting to various scenarios, whereas MPC relies on a predefined mathematical model to solve optimization problems in real-time. Despite their widespread use, there is a lack of direct comparative analysis under standardized conditions. This work addresses this gap by benchmarking MPC and RL controllers on a Unitree Go1 quadruped robot within the MuJoCo simulation environment, focusing on a standardized task, straight walking at a constant velocity. Performance is evaluated based on disturbance rejection, energy efficiency, and terrain adaptability. The results show that RL excels in handling disturbances and maintaining energy efficiency but struggles with generalization to new terrains due to its dependence on learned policies tailored to specific environments. In contrast, MPC shows enhanced recovery capabilities from larger perturbations by leveraging its optimization-based approach, allowing for a balanced distribution of control efforts across the robot’s joints. The results present the advantages and limitations of both RL and MPC, offering insights into selecting an appropriate control strategy for legged robotic applications.

This paper uses results from geometric mechanics and control to determine the degree of coupling between actuated and unactuated degrees of freedom in a two-link biped robot. By comparing the degree of coupling when ankle actuation is used and when hip actuation is used, it is clear that ankle actuation affords stronger dynamic coupling and hence, may provide a superior means for control design for robust gait and posture control. This is true both in the case where the robot is configured as a bipedal walker and the case where it is configured to model posture control. In the case of posture control, these results are consistent with some literature on the means by which humans maintain posture.

This paper presents an approach to show global controllability of a class of underactuated mechanical systems. This class of systems include gymnastic robots and the classic cart-pole system. For this class of systems, we can define a connection point, and design a damping controller $u(t)$ with the Lyapunov method to drive all states to the connection point. Further by exploiting the time reversal symmetry of the system and spline interpolation, a controller $u(-t)$ can be obtained to drive the system from the connection point to any other state. The system is thus shown completely controllable, i.e., there exists an admissible trajectory from any given state to any given final state. Swing-up control designs for a pendubot, cart-pole system and triple pendulum are given as illustrative examples.