Ground reaction force sensor fault detection and recovery method based on virtual force sensor for walking biped robots

This paper presents a novel method for ground force sensor faults detection and faulty signal reconstruction using Virtual force Sensor (VFS) for slow walking bipeds. The design structure of the VFS consists of two steps, the total ground reaction force (GRF) and its location estimation for each leg based on the center of mass (CoM) position, the leg kinematics, and the IMU readings is carried on in the first step. In the second step, the optimal estimation of the distributed reaction forces at the contact points in the feet sole of walking biped is carried on. For the optimal estimation, a constraint model is obtained for the distributed reaction forces at the contact points and the quadratic programming optimization method is used to solve for the GRF. The output of the VFS is used for fault detection and recovery. A faulty signal model is formed to detect the faults based on a threshold, and recover the signal using the VFS outputs. The sensor offset, drift, and frozen output faults are studied and tested. The proposed method detects and estimates the faults and recovers the faulty signal smoothly. The validity of the proposed estimation method was confirmed by simulations on 3D dynamics model of the humanoid robot SURALP while walking. The results are promising and prove themselves well in all of the studied fault cases

Investigations of Model-Free Sliding Mode Control Algorithms including Application to Autonomous Quadrotor Flight

Sliding mode control is a robust nonlinear control algorithm that has been used to implement tracking controllers for unmanned aircraft systems that are robust to modeling uncertainty and exogenous disturbances, thereby providing excellent performance for autonomous operation. A significant advance in the application of sliding mode control for unmanned aircraft systems would be adaptation of a model-free sliding mode control algorithm, since the most complex and time-consuming aspect of implementation of sliding mode control is the derivation of the control law with incorporation of the system model, a process required to be performed for each individual application of sliding mode control. The performance of four different model-free sliding mode control algorithms was compared in simulation using a variety of aerial system models and real-world disturbances (e.g. the effects of discretization and state estimation). The two best performing algorithms were shown to exhibit very similar behavior. These two algorithms were implemented on a quadrotor (both in simulation and using real-world hardware) and the performance was compared to a traditional PID-based controller using the same state estimation algorithm and control setup. Simulation results show the model-free sliding mode control algorithms exhibit similar performance to PID controllers without the tedious tuning process. Comparison between the two model-free sliding mode control algorithms showed very similar performance as measured by the quadratic means of tracking errors. Flight testing showed that while a model-free sliding mode control algorithm is capable of controlling realworld hardware, further characterization and significant improvements are required before it is a viable alternative to conventional control algorithms. Large tracking errors were observed for both the model-free sliding mode control and PID based flight controllers and the performance was characterized as unacceptable for most applications. The poor performance of both controllers suggests tracking errors could be attributed to errors in state estimation, which effectively introduce unknown dynamics into the feedback loop. Further testing with improved state estimation would allow for more conclusions to be drawn about the performance characteristics of the model-free sliding mode control algorithms

Nondeterministic hybrid dynamical systems

This thesis is concerned with the analysis, control and identification of hybrid dynamical systems. The main focus is on a particular class of hybrid systems consisting of linear subsystems. The discrete dynamic, i.e., the change between subsystems, is unknown or nondeterministic and cannot be influenced, i.e. controlled, directly. However changes in the discrete dynamic can be detected immediately, such that the current dynamic (subsystem) is known. In order to motivate the study of hybrid systems and show the merits of hybrid control theory, an example is given. It is shown that real world systems like Anti Locking Brakes (ABS) are naturally modelled by such a class of linear hybrids systems. It is shown that purely continuous feedback is not suitable since it cannot achieve maximum braking performance. A hybrid control strategy, which overcomes this problem, is presented. For this class of linear hybrid system with unknown discrete dynamic, a framework for robust control is established. The analysis methodology developed gives a robustness radius such that the stability under parameter variations can be analysed. The controller synthesis procedure is illustrated in a practical example where the control for an active suspension of a car is designed. Optimal control for this class of hybrid system is introduced. It is shows how a control law is obtained which minimises a quadratic performance index. The synthesis procedure is stated in terms of a convex optimisation problem using linear matrix inequalities (LMI). The solution of the LMI not only returns the controller but also the performance bound. Since the proposed controller structures require knowledge of the continuous state, an observer design is proposed. It is shown that the estimation error converges quadratically while minimising the covariance of the estimation error. This is similar to the Kalman filter for discrete or continuous time systems. Further, we show that the synthesis of the observer can be cast into an LMI, which conveniently solves the synthesis problem

Locally Optimal Estimation and Control of Cable Driven Parallel Robots using Time Varying Linear Quadratic Gaussian Control

We present a locally optimal tracking controller for Cable Driven Parallel Robot (CDPR) control based on a time-varying Linear Quadratic Gaussian (TV-LQG) controller. In contrast to many methods which use fixed feedback gains, our time-varying controller computes the optimal gains depending on the location in the workspace and the future trajectory. Meanwhile, we rely heavily on offline computation to reduce the burden of online implementation and feasibility checking. Following the growing popularity of probabilistic graphical models for optimal control, we use factor graphs as a tool to formulate our controller for their efficiency, intuitiveness, and modularity. The topology of a factor graph encodes the relevant structural properties of equations in a way that facilitates insight and efficient computation using sparse linear algebra solvers. We first use factor graph optimization to compute a nominal trajectory, then linearize the graph and apply variable elimination to compute the locally optimal, time varying linear feedback gains. Next, we leverage the factor graph formulation to compute the locally optimal, time-varying Kalman Filter gains, and finally combine the locally optimal linear control and estimation laws to form a TV-LQG controller. We compare the tracking accuracy of our TV-LQG controller to a state-of-the-art dual-space feed-forward controller on a 2.9m x 2.3m, 4-cable planar robot and demonstrate improved tracking accuracies of 0.8{\deg} and 11.6mm root mean square error in rotation and translation respectively.Comment: 8 pages, 11 figures, accepted to IEEE International Conference on Intelligent Robotics and Systems (IROS) 202

Controlling a contactless planar actuator with manipulator

An existing magnetically levitated planar actuator with manipulator has been studied and improved from a control point of view. This prototype consists of a magnetically levitated six-degree-of-freedom (6-DOF) planar actuator with moving magnets, with a 2-DOF manipulator on top of it. This system contains three different contactless technologies: contactless bearing and propulsion of the planar actuator, wireless powering of the manipulator, and wireless communication and control of the manipulator. The planar actuator (PA) consists of a Halbach magnet array, which is levitated and controlled in all six DOF’s above a stationary coil array. The PA is propelled in two horizontal translational DOF’s while the other four DOF’s are stabilized to accomplish a stiff bearing. Each active coil contributes to the production of forces and torques acting on the magnet array. Since the number of active coils is much larger than the number of DOF’s, the desired force production can be distributed over many coils. Therefore, a commutation algorithm has to be used to invert the mapping of the forces and torques exerted by the set of active coils as a function of the coil currents and the position and orientation of the translator. One method for linearization and decoupling of the forces and torques was developed in the past. The method is called direct wrench decoupling and guaranties minimal dissipation of energy. However, no constraints on the maximum current can be given. This study proposes two novel, norm-based commutation methods: l8-norm and clipped l2-norm based commutation. Both methods can put bounds on the maximum currents in the coils to prevent saturation of the current amplifiers. The first method focuses on minimization of the maximum current whereas the second method limits the peak current while it minimizes the power losses. Consequently, a higher acceleration of the translator can be achieved and/or less powerful (cheaper) current amplifiers can be utilized and/or fewer commutation errors arise. Only a long-stroke translational movement of the moving magnet planar actuators has been considered in the past. The possibility of a completely propelled and controlled rotation about the vertical axis instead of just stabilizing it for bearing has been analyzed in this thesis from a control point of view. Enhancing the planar actuator with a long-range rotation will increase its utility value and opens new application areas. Based on this investigation, a novel coil array with a triangular grid of rounded coils has been proposed for better controllability in any orientation of the PA. In addition, other coil and magnet topologies have been studied from a control point of view for their suitability for full rotation. The influence of different kinds of error-causes on the commutation precision has been studied. From this investigation, it has been found that the offsets of the measurement system have the highest influence on the precision of the commutation. Investigation of the convergence of the procedure for estimation and elimination of these offsets has been performed. Although it was not proven that the procedure could be applied on the whole workspace of the PA, the convergence has been shown at least for all the investigated points. From this investigation, convergence for any position in the workspace of the PA is expected. It was found that it is possible to use the procedure also with different topologies and with different commutations. A novel wireless link has been developed for the real-time control of a fast motion system. The wireless link communicates via infrared-light transceivers and the link has a delay and a packet-loss ratio almost indistinguishable from the wired connection for the bandwidth of the system up to several kilohertz. The clipped l2-norm based commutation method has been successfully tested on the experimental setup after improving the measurement system, the contactless energy transfer and the wireless communication. With a new, interferometer sensor system, a well-controlled PA with two long-stroke DOF’s has become available. Improved contactless energy transfer does not cause increased electromagnetic interference during switching between the primary coils any more and the wireless connection using the infrared link provides a reliable communication channel between the manipulator and the fixed world. Several control approaches have been tested on the experimental setup. Both, the classical PID control, Sliding-mode control and Iterative learning control have been implemented. Each controller brought better performance than the previous one. Also, a fourth-order trajectory and enhanced feedforward control helped to improve performance. Finally, the tracking errors, in comparison to the initial situation, were reduced by a factor 10 (and even more than by a factor 50 with deactivated contactless energy transfer) while the velocity and acceleration of the system were a factor 4 and 14, respectively, higher