Publications

This paper introduces a methodology for computing artificial vector fields designed to ensure the convergence and circulation of trajectories to a curve in the pose space. Extending the work from Rezende et al. (2022) to incorporate orientations, we define a normal vector that asymptotically guides a trajectory to the desired curve, and a tangent vector that ensures circulation. By employing this vector field methodology, we achieve an autonomous closed-loop system with integrated path planning and control. Our approach is applied within a decentralized adaptive control to guide a rigid body with unknown parameters using a team of agents, ensuring compliance with a target pose curve.

This work introduces a novel vector field strategy for controlling systems on connected matrix Lie groups, ensuring both convergence to and circulation around a curve defined on the group. Our approach generalizes the framework presented in Rezende et al.(2022) and reduces to it when applied to the Lie group of translations in Euclidean space. Building upon the key properties from Rezende et al.(2022), such as the orthogonality between convergent and circulating components, we extend these results by exploiting additional Lie group properties. Notably, our method ensures that the control input is non-redundant, matching the dimension of the Lie group rather than the potentially larger dimension of the embedding space. This leads to more practical control inputs in certain scenarios. A significant application of this strategy is in controlling systems on SE (3), where the non-redundant input corresponds to the mechanical twist of the object. This makes the method particularly well-suited for controlling systems with both translational and rotational freedom, such as omnidirectional drones. We also present an efficient algorithm for computing the vector field in this context. Furthermore, the strategy is applied as a high-level kinematic controller in a collaborative manipulation task, where six agents manipulate a large object with unknown parameters in the Lie group R3 x SO (3). A low-level dynamic adaptive controller guarantees that the velocity tracking error between the system and the kinematic controller output converges to zero, a result supported by theoretical proofs. Simulation results validate the effectiveness of the proposed method in both the kinematic scenario and the integration of kinematic and dynamic controllers.