Wouter Wolfslag

Optimization of feedforward controllers to minimize sensitivity to model inaccuracies

The common view on feedforward control is that it needs an accurate model in order to accurately predict a future state of the system. However, in this paper we show that there are model inaccuracies that do not affect the final position of a motion, when using the right feedforward controller. Having an accurate final position is the main requirement in the task we consider: a pick-and-place task. We optimized the feedforward controllers such that the effect of model inaccuracies on the final position was minimized. The system we studied is a one DOF robotic arm in the horizontal plane, of which we show simulation and hardware results. The results show that the errors in the final position can be reduced to approximately zero for an inaccurate Coulomb, viscous or torque dependent friction. Furthermore, errors in the final position can be reduced, but not to zero, for an inaccurate inertia or motor constant. In conclusion, we show that for certain model inaccuracies, no feedback is required to eliminate the effect of an inaccurate model on the final position of a motion.

Open loop stable control in repetitive manipulation tasks

Most conventional robotic arms depend on sensory feedback to perform their tasks. When feedback is inaccurate, slow or otherwise unreliable, robots should behave more like humans: rely on feedforward instead. This paper presents an approach to perform repetitive tasks with robotic arms, without the need for feedback (i.e. the control is open loop). The cyclic motions of the repetitive tasks are analyzed using an approach similar to limit cycle theory. We optimize open loop control signals that result in open loop stable motions. This approach to manipulator control was implemented on a two DOF arm in the horizontal plane with a spring on the first DOF, of which we show simulation and hardware results. The results show that both in simulation and in hardware experiments, it is possible to create open loop stable cycles. However, the two resulting cycles are different due to model inaccuracies. We also show simulation and hardware results for an inverted pendulum, of which we have a more accurate model. These results show stable cycles that are the same in simulation and hardware experiments.

Robust feedforward control of robotic arms with friction model uncertainty

To design feedforward controllers for robots, a model that includes friction is important. However, friction is hard to identify, which causes uncertainty in the model. In this paper we consider rest-to-rest motions of robotic arms that use only feedforward control. We show that it is possible to design feedforward controllers such that the final position of the motion is robust to uncertainty in the friction model. We studied a one DOF robotic arm in the horizontal plane, of which we show analytical, simulation and hardware results and we also show simulation results of a planar two DOF arm. Our friction model includes three types of friction: viscous, Coulomb and torque dependent friction. The results show that it is possible to eliminate the sensitivity of the final state to uncertainty in the three types of friction. We consider feedforward controlled rest-to-rest motions of robotic arms.The final positions of the motions are robust to uncertainty in the friction model.We study one and two DOF arms and perform analytical, numerical and hardware studies.Robust motions first move away from the goal position before moving towards it.

Distance metric approximation for state-space RRTs using supervised learning

The dynamic feasibility of solutions to motion planning problems using Rapidly Exploring Random Trees depends strongly on the choice of the distance metric used while planning. The ideal distance metric is the optimal cost of traversal between two states in the state space. However, it is computationally intensive to find the optimal cost while planning. We propose a novel approach to overcome this barrier by using a supervised learning algorithm that learns a nonlinear function which is an estimate of the optimal cost, via offline training. We use the Iterative Linear Quadratic Regulator approach for estimating an approximation to the optimal cost and learn this cost using Locally Weighted Projection Regression. We show that the learnt function approximates the original cost with a reasonable tolerance and more importantly, gives a tremendous speed up of a factor of 1000 over the actual computation time. We also use the learnt metric for solving the pendulum swing up planning problem and show that our metric performs better than the popularly used Linear Quadratic Regulator based metric.

Clutched Elastic Actuators

This paper identifies the class of actuators called clutched elastic actuators (CEAs). CEAs use clutches to control the energy flow into springs. CEAs in exoskeletons, prostheses, legged robots, and robotic arms have shown the ability to reduce the energy consumption and motor requirements, such as peak torque and peak power. Because of those abilities, they are increasingly used in robotics. In this paper, we categorize existing CEA designs, identify trends in those designs, and provide a method to analyze their functionality. Based on a literature survey, current CEA designs are placed in nine categories, depending on their morphology. The main trend is that CEA designs are becoming more complex, meaning that the number of clutches and springs increases. We show with the introduced mathematical analysis that the functionality can be analyzed with a constraint matrix, a stiffness matrix, and multiplication of a clutch-dependent diagonal matrix with an oriented incidence matrix. This method eases the analysis of the functionality of CEAs. Furthermore, it can lead to new CEA designs in which the number of resulting stiffnesses grows exponentially with the number of springs and clutches.

Learning robustly stable open-loop motions for robotic manipulation

Robotic arms have been shown to be able to perform cyclic tasks with an open-loop stable controller. However, model errors make it hard to predict in simulation what cycle the real arm will perform. This makes it difficult to accurately perform pick and place tasks using an open-loop stable controller. This paper presents an approach to make open-loop controllers follow the desired cycles more accurately. First, we check if the desired cycle is robustly open-loop stable, meaning that it is stable even when the model is not accurate. A novel robustness test using linear matrix inequalities is introduced for this purpose. Second, using repetitive control we learn the open loop controller that tracks the desired cycle. Hardware experiments show that using this method, the accuracy of the task execution is improved to a precision of 2.5?cm, which suffices for many pick and place tasks. Stable open-loop control of pick and place robots that handles model inaccuracies.Find robustly stable trajectory, then learn the tracking input online.Novel linear matrix inequalities based approach to determine robustness.Using Repetitive Control an open loop accuracy of 2.5?cm was obtained.

The effect of the choice of feedforward controllers on the accuracy of low gain controlled robots

High feedback gains cannot be used on all robots due to sensor noise, time delays or interaction with humans. The problem with low feedback gain controlled robots is that the accuracy of the task execution is potentially low. In this paper we investigate if trajectory optimization of feedback-feedforward controlled robots improves their accuracy. For rest-to-rest motions, we find the optimal trajectory indirectly by numerically optimizing the corresponding feedforward controller for accuracy. A new performance measure called the Manipulation Sensitivity Norm (MSN) is introduced that determines the accuracy under most disturbances and modeling errors. We tested this method on a two DOF robotic arm in the horizontal plane. The results show that for all feedback gains we tested, the choice for the trajectory has a significant influence on the accuracy of the arm (viz. position errors being reduced from 2.5 cm to 0.3 cm). Moreover, to study which features of feedforward controllers cause high or low accuracy, four more feedforward controllers were tested. Results from those experiments indicate that a trajectory that is smooth or quickly approaches the goal position will be accurate.