Foldable, origami-inspired, and laminate mechanisms are highly susceptible to deformation under external loading, which can lead to position or orientation errors if idealized kinematic models are used. According to dimensional scaling laws, laminate devices can often be treated as rigid bodies at millimeter and smaller scale deformations. However, foldable mechanisms enter the territory of soft robots at larger scales. In this paper, we show the effect of external loads applied to a laminate, 2-DOF parallel robot and the corresponding errors during a pointing task. We then present two control methods, based on deep learning, that compensates for errors caused by the material deformation in foldable robots. For each proposed control method, a Deep Neural Network (DeepNN) is trained to learn the end-effector's deformation model in no-load and loaded conditions. A DeepNN called an updating network is trained and applied in real-time using measured sensor data, in order to transfer updated weights into another DeepNN called the target network. The target network generates control signals with the aim of compensating for the end-effector's error in tracking a desired trajectory. We evaluate our proposed control methods when applied to a laminate robotic end-effector under different external loading conditions in tracking spiral paths. The experimental results show the effectiveness of our proposed control methods in compensating for material deformation in foldable robots.

In this paper, we present a decentralized control approach based on a Nonlinear Model Predictive Control (NMPC) method that employs barrier certificates for safe navigation of multiple nonholonomic wheeled mobile robots in unknown environments with static and/or dynamic obstacles. This method incorporates a Learned Barrier Function (LBF) into the NMPC design in order to guarantee safe robot navigation, i.e., prevent robot collisions with other robots and the obstacles. We refer to our proposed control approach as NMPC-LBF. Since each robot does not have a priori knowledge about the obstacles and other robots, we use a Deep Neural Network (DeepNN) running in real-time on each robot to learn the Barrier Function (BF) only from the robot's LiDAR and odometry measurements. The DeepNN is trained to learn the BF that separates safe and unsafe regions. We implemented our proposed method on simulated and actual Turtlebot3 Burger robot(s) in different scenarios. The implementation results show the effectiveness of the NMPC-LBF method at ensuring safe navigation of the robots.

In this paper, we present an optimal control approach using Linear Matrix Inequalities (LMIs) for trajectory tracking control of a three-wheeled omnidirectional mobile robot in the presence of external disturbances on the robot's actuators and noise in the robot's sensor measurements. First, a state-space representation of the omnidirectional robot dynamics is derived using a point-mass dynamic model. Then, we propose an LMI-based full-state feedback H∞-optimal controller for the tracking problem. The robot's tracking performance with the H∞-optimal controller is compared to its performance with a classical full-state feedback tracking controller in simulations with circular and bowtie-shaped reference trajectories. In order to evaluate our proposed controller in practice, we also implement the H∞-optimal and classical controllers for these reference trajectories on a three-wheeled omnidirectional robot. The H∞-optimal controller guarantees stabilization of the robot motion and attenuates the effects of frictional disturbances and measurement noise on the robot's tracking performance. Using the H∞-optimal controller, the robot is able to track the reference trajectories with up to a 47.8% and 45.8% decrease in the maximum pose and twist errors, respectively, over a full cycle of the trajectory compared to the classical controller. The simulation and experimental results show that our LMI-based H∞-optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.