Cardinal Exponential Splines: Part II—Think Analog, Act Digital

By interpreting the Green-function reproduction property of exponential splines in signal processing terms, we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts. The link is that the latter are the B-spline coefficients of the former (which happen to be exponential splines). Motivated by this observation, we introduce an extended family of cardinal splines—the generalized E-splines—to generalize the concept for all convolution operators with rational transfer functions. We construct the corresponding compactly-supported B-spline basis functions, which are characterized by their poles and zeros, thereby establishing an interesting connection with analog filter design techniques. We investigate the properties of these new B-splines and present the corresponding signal processing calculus, which allows us to perform continuous-time operations, such as convolution, differential operators, and modulation, by simple application of the discrete version of these operators in the B-spline domain. In particular, we show how the formalism can be used to obtain exact, discrete implementations of analog filters. Finally, we apply our results to the design of hybrid signal processing systems that rely on digital filtering to compensate for the nonideal characteristics of real-world analog-to-digital (A-to-D) and D-to-A conversion systems

Coupling of Simulink Controller and Robot Simulation for Simulating Compliant Contacts with the Environment

Humanoid robots often have a larger spectrum of abilities and requirements compared to specialized industry robots and interact with their environment in different and more complex ways. This comes with challenges when implementing and testing their behavior. Digital representations of these robots are often used to plan or visualize behavior but rarely to physically simulate movement as a way to develop a digital twin that also behaves identically in any scenario given the same input. This thesis addresses the coupling of the existing controller of DLR’s humanoid robot Rollin’ Justin with a physics simulation, allowing for the reproduction, prediction and measurement of the robot’s torque-controlled behavior and its contact forces to the environment. The compliant controller reactions to these contacts are crucial to the success of many robotic tasks. The fully physics-driven simulation also makes it possible to test scenarios in advance and to make behavior predictions of the real robot, even in cases of uncertainty regarding the surrounding. Shifting the testing of scenarios or controller changes to the simulation can avoid the time and financial efforts of executions on the physical robot, which possibly even damage parts of it. We improved the robot model used in the simulation, defined communication interfaces between the controller and the simulation and implemented the actuation logic, converting the pre-existing kinematic simulation behavior to a torque-driven one. For the evaluation of the coupled system we measured the tracking accuracy of the simulated model in regard to recorded data from the real robot and conducted an experiment with environment contacts. The digital twin shows good tracking accuracy, joint and end effector positions are replicated well. Forces in contact with the environment are at similar magnitudes as observed in reality. The experiment also demonstrates the usage of multiple simulated environment states to predict outcomes in cases of uncertainty