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Beyond the Cascade: Juggling Vanilla Siteswap Patterns
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Robots that can learn in the physical world will be important to enable robots to escape their stiff and pre-programmed movements. For dynamic high-acceleration tasks, such as juggling, learning in the real-world is particularly challenging as one must push the limits of the robot and its actuation without harming the system, amplifying the necessity of sample efficiency and safety for robot learning algorithms. In contrast to prior work which mainly focuses on the learning algorithm, we propose a learning system, that directly incorporates these requirements in the design of the policy representation, initialization, and optimization. We demonstrate that this system enables the high-speed Barrett WAM manipulator to learn juggling two balls from 56 minutes of experience with a binary reward signal. The final policy juggles continuously for up to 33 minutes or about 4500 repeated catches. The videos documenting the learning process and the evaluation can be found at https://sites.google.com/view/jugglingbot
We introduce Pinocchio, an open-source software framework that implements rigid body dynamics algorithms and their analytical derivatives. Pinocchio does not only include standard algorithms employed in robotics (e.g., forward and inverse dynamics) but provides additional features essential for the control, the planning and the simulation of robots. In this paper, we describe these features and detail the programming patterns and design which make Pinocchio efficient. We evaluate the performances against RBDL, another framework with broad dissemination inside the robotics community. We also demonstrate how the source code generation embedded in Pinocchio outperforms other approaches of state of the art.
Entertainment robots in theme park environments typically do not allow for physical interaction and contact with guests. However, catching and throwing back objects is one form of physical engagement that still maintains a safe distance between the robot and participants. Using a theme park type animatronic humanoid robot, we developed a test bed for a throwing and catching game scenario. We use an external camera system (ASUS Xtion PRO LIVE) to locate balls and a Kalman filter to predict ball destination and timing. The robot's hand and joint-space are calibrated to the vision coordinate system using a least-squares technique, such that the hand can be positioned to the predicted location. Successful catches are thrown back two and a half meters forward to the participant, and missed catches are detected to trigger suitable animations that indicate failure. Human to robot partner juggling (three ball cascade pattern, one hand for each partner) is also achieved by speeding up the catching/throwing cycle. We tested the throwing/catching system on six participants (one child and five adults, including one elderly), and the juggling system on three skilled jugglers.
We describe a new physics engine tailored to model-based control. Multi-joint dynamics are represented in generalized coordinates and computed via recursive algorithms. Contact responses are computed via efficient new algorithms we have developed, based on the modern velocity-stepping approach which avoids the difficulties with spring-dampers. Models are specified using either a high-level C++ API or an intuitive XML file format. A built-in compiler transforms the user model into an optimized data structure used for runtime computation. The engine can compute both forward and inverse dynamics. The latter are well-defined even in the presence of contacts and equality constraints. The model can include tendon wrapping as well as actuator activation states (e.g. pneumatic cylinders or muscles). To facilitate optimal control applications and in particular sampling and finite differencing, the dynamics can be evaluated for different states and controls in parallel. Around 400,000 dynamics evaluations per second are possible on a 12-core machine, for a 3D homanoid with 18 dofs and 6 active contacts. We have already used the engine in a number of control applications. It will soon be made publicly available.
Humans can perform fast and skillful manipulations using various parts of the body by effectively utilizing the dynamics of the targets. Visual sensation is the most important human sense used for such manipulations. Juggling is one such example involving skillful and dynamic manipulations, and visual information is essential for it to be successful. Previously, there have been several studies about robotic juggling. However, none of these studies have considered cases in which a human-like multifingered hand-arm is used for the robotic juggling. The purpose of this study is to achieve two-ball juggling using our robotic hand-arm, which has three general purpose fingers, and stereo vision. Image processing is executed at 500 fps using a high-speed vision system and graphics processing unit (GPU). The trajectory of the robotic hand-arm is generated based on the ball's estimated dropping position and moment, and the robot catches the ball. The juggling motion is achieved by repeating this cycle. Therefore, the results show that the robot successfully juggles two balls using our hand-arm system.
Recent results of dynamical systems theory are used to derive
strong predictions concerning the global properties of a simplified
model of a planar juggling robot. In particular, it is found that
certain lower-order local (linearized) stability properties determine
the essential global (nonlinear) stability properties, and that
successive increments in the controller gain settings give rise to a
cascade of stable period-doubling bifurcations that comprise a universal
route to chaos. The theoretical predictions are verified by simulation
and corroborated by experimental data from the juggling robot
A spatial two-juggle is discussed. The device has the ability to
bat two freely falling balls into stable periodic vertical trajectories
with a single three degree-of-freedom robot arm using a real-time stereo
camera system for sensory input. After a brief review of a
previously-reported one-juggle, the author's initial approach to the
two-juggle planning and control problem is described. A number of
important refinements to their initial strategy are given. Data from
typical two-juggle runs in the laboratory are given
Discusses robot motion planning in dynamic environment, that is,
generation of a motion pattern to attain a working purpose. The authors
examine the relation between this redundancy and the dynamic dexterity
of robots. Especially the authors focus on `juggling' as a typical
example of such a working purpose(task). To juggle several balls in the
gravitational field, the motion of the robot is determined considering
the dynamic property of balls. It is shown that a parametric
representation of the robot motion makes it easy to generate an
appropriate trajectory of the end-effector for `juggling task'
A new class of control algorithms—the “mirror algorithms”— gives rise to experimentally observed juggling and catching behavior in a planar robotic mechanism. The simplest of these algorithms (on which all the others are founded) is provably correct with respect to a simplified model of the robot and its environment. This article briefly reviews the physical setup and underlying mathematical theory. It discusses two significant extensions of the fundamental algorithm to juggling two objects and catching. We provide data from successful empirical verifi cations of these control strategies and briefly speculate on the larger implications for the field of robotics.
For more information: Kod*Lab
We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.
We present a primal-dual interior-point algorithm with a lter line-search method for non- linear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the fea- sibility restoration phase for the lter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlin- ear programming.
The model of the juggler is a mechanical machinery designed and constructed to demonstrate and teach control of fast and highly effective servo drives that are commonly used in various motion control applications in industry. The aim of this project is to create a control system able to juggle with three billiard balls, close a visual feedback to recognise actual position of individual balls and present procedures that can be used to design and control similar systems in industrial applications.
Open-loop stable control strategies for a variety of juggling
tasks are explored. The specific tasks studied are paddle juggling,
ball-in-a-wedge juggling, five ball juggling, and devil sticking. All
dynamic tasks introduced are solved by special purpose systems. The
results of these investigations may provide insight into how open loop
control can serve as a useful foundation for closed loop control and,
particularly, what to focus on in learning control
The mathematics of juggling
- B Polster
Shannon (robot) juggling: 3 and 5 balls
- C Atkeson