Diffusion generative modeling has become a promising approach for learning robotic manipulation tasks from stochastic human demonstrations. In this paper, we present Diffusion-EDFs, a novel SE(3)-equivariant diffusion-based approach for visual robotic manipulation tasks. We show that our proposed method achieves remarkable data efficiency, requiring only 5 to 10 human demonstrations for effective end-to-end training in less than an hour. Furthermore, our benchmark experiments demonstrate that our approach has superior generalizability and robustness compared to state-of-the-art methods. Lastly, we validate our methods with real hardware experiments. Project Website: https://sites.google.com/view/diffusion-edfs

In this paper, we introduce a novel approach for designing invariant control laws through potential functions for fully actuated dynamical systems evolving on manifolds by leveraging the power of neural networks. The geometry and non-linearity inherent to manifold-based dynamical systems pose challenges for traditional control law design, necessitating techniques with the interplay of differential geometry and dynamical systems for ensuring stability. Apart from stability, performance and optimality are other challenging areas to address for dynamical systems evolving on manifolds. On top of these, the concept of invariance helps us improve learning transferability skills from one scene to another scene. We propose invariant potential functions on manifolds defined by neural networks that can be used to generate elastic forces for asymptotic tracking of trajectories. The weights of the potential function can be tuned to shape the potential functions according to the performance requirements through minimizing a loss function.

In an age of ever-increasing penetration of Global Positioning System-enabled mobile devices, the potential of real-time “probe” location information for estimating the state of transportation networks is receiving increasing attention. Much work has been done on using probe data to estimate the current speed of vehicle traffic (or, equivalently, trip travel time). While travel times are useful to individual drivers, the state variable for a large class of traffic models and control algorithms is vehicle density. Our goal is to use probe data to supplement traditional fixed-location loop detector data for density estimation. To this end, we derive a method based on Rao-Blackwellized particle filters, a sequential Monte Carlo scheme. We present a simulation where we obtain a 30% reduction in density mean absolute percentage error from fusing loop and probe data versus using loop data alone. We also present results using real data from a 19-mi freeway section in Los Angeles, CA, where we obtain a 31% reduction. In addition, our method's estimate when using only the real-world probe data and no loop data outperformed the estimate produced when only loop data were used (i.e., an 18% reduction). These results demonstrate that probe data can be used for traffic density estimation.

Abstract In this paper the operation and transit of emergency vehicles on an Automated Highway System (AHS) designed under the control architecture proposed in the California PATH program is described. The term emergency vehicles is used in a general sense to describe vehicles, such as police cars, ambulances and tow trucks, that may service faults inside or outside the AHS. The transit of emergency vehicles requires intensive participation of the Coordination layer, which directs the interactions of neighboring vehicles, and the Link layer, which regulates traffic flow along stretches of highway. In this paper, we describe various strategies for these two hierarchical layers that are needed to assign high priority transit to emergency vehicles on the AHS. These Coordination and Link layer maneuvers circulate vehicles around the emergency vehicle in both free flowing and stopped traffic.

A decoupled controller architecture and discrete time pole placement design methodology is proposed for dual-stage servo controller design of magnetic hard disk drives. The methodology was applied to the controller design of a dual-stage servo with a MEMS microactuator (MA) which rotates the slider relative to the gimbal. MIMO and SIMO controllers were designed for cases when the microactuator's relative position error signal is respectively available and not available to the control system. The effects of MA resonance variations on the stability and performance of the controller were analyzed for both cases.

Describes the design of an automated highway system (AHS) developed over the past ten years in the California PATH program. The AHS is a large, complex system, in which vehicles are automatically controlled. The design and implementation of the AHS required advances in actuator and sensor technologies, as well as the design, analysis, simulation, and testing of large-scale, hierarchical hybrid control systems. The paper focuses on the multilayer AHS control architecture and some questions of implementation. It discusses in detail the design and safety verification of the on-board vehicle control system and the design of the link-layer traffic-flow controller.

Two concepts are advocated for the task specification and control of mechanical manipulators: 1) coding tasks in terms of velocity fields; 2) designing controllers so that the manipulator when under feedback control, interacts in an energetically passive manner with its physical environment. Based on these two concepts, a new passive velocity field controller is proposed which mimics the behavior of a passive energy storage element, such as a flywheel or a spring. It stores and releases energy while interacting with the manipulator, but does not generate any. The controller has the interesting property that it stabilizes any multiple (positive or negative) of the desired velocity field, and exponentially stabilizes the particular multiple of the desired velocity field which is determined by the total kinetic energy of the manipulator control system.

This paper presents repetitive and adaptive motion control schemes for rigid-link robot manipulators, when the manipulator's joint velocities cannot be measured by the control system. The control objective consists in tracking a prescribed desired trajectory. In the case of repetitive control, the desired trajectory is periodic and it is required that the robot achieve the control objective through repeated learning trials. We assume that the robot inverse dynamics are totally unknown, except that they can be represented by an integral of the product of known differentiable kernel and an unknown influence function. In the case of adaptive control, it is assumed that only the manipulator inertia parameters are unknown and that the desired trajectory jerks are available to the control system. In both control schemes, a velocity observer, which is formulated based on the desired input/output relation of the manipulator, is used to estimate the manipulator joint velocities. A stability analysis of the repetitive and adaptive control schemes with velocity estimation is presented. Simulation and experimental results show that the proposed repetitive control algorithm is successful in achieving the control objective without direct measurement of the joint velocities.

Two concepts for the task specification and control for mechanical manipulators are advocated: the coding of tasks in terms of velocity fields; and controllers that maintain the passivity relationship between the manipulator and its physical environment. A passive velocity field tracking controller is proposed. The proposed dynamic controller mimics a flywheel: it stores and releases energy to the manipulator, but does not generate any. The controller has the interesting property that it stabilizes any multiple (positive or negative) of the desired velocity field, and exponentially stabilizes the particular multiple which is related to the total kinetic energy of the manipulator+controller.

A method for nonlinear function identification and its application to learning control are presented. The control objective is to identify and compensate for a nonlinear disturbance function. The nonlinear disturbance function is represented as an integral of a predefined kernel function multiplied by an unknown influence function. Sufficient conditions for the existence of such a representation are provided. The learning rule indirectly estimates the unknown function by updating an influence function estimate. It is shown that the controller achieves the disturbance cancellation asymptotically. The method is extended to the repetitive control of robot manipulators. Simulation and actual real-time implementation results using the Berkeley/NSK robot arm show that the proposed learning is more robust and converges at a faster rate than conventional repetitive controllers.>

An exponentially stable direct adaptive control law for motion control of robot manipulators is presented. This control law utilizes the desired trajectory information instead of the actual manipulator joint signals for feedforward compensations and parameter adaptation. Computationally, it is extremely efficient. The exponential stability of the adaptive control algorithm is proven without requiring the persistent excitation condition and by fully considering the nonlinear dynamics of the manipulator in the analysis.>

The digital implementation of two repetitive control schemes on a SCARA-type two-axes manipulator is described. The controllers consist of a linear proportional and derivative feedback term and a feedforward repetitive term. The repetitive feedforward is adjusted periodically by using a linear combination of the position and velocity tracking errors of the current and/or previous cycles. Explicit knowledge of the structure of the manipulator model is not required. Two different learning algorithms for updating the feedforward repetitive control action are investigated. A simulation is first conducted to evaluate the performance of the repetitive controllers. The implementation of the controllers on the Berkeley/NSK SCARA robot arm is then discussed. Simulation and implementation results are in agreement and show that the use of the repetitive feedforward action in the control scheme significantly improves the tracking performance of the robot.>

A hybrid direct adaptive motion control law for robot manipulators is presented. The algorithm is hybrid in the sense that the linear portion of the controller is continuous-time, while the parameter adaptation law is discrete-time. The algorithm utilizes the desired joint signals instead of the actual manipulator joint signals in the computation of the control and parameter adaptation laws. The algorithm is extremely computationally efficient when the desired trajectories are known in advance. The stability of the algorithm is proven utilizing the full nonlinear model of the manipulator in the analysis, and without linearization of the manipulator dynamic equations. The full digital implementation of this algorithm is also discussed, and experimental results on the control of a two-degree-of-freedom SCARA arm are presented.>

Utilizing the fact that a manipulator composed of rigid links is a passive system, an approach based on the properties of interconnected passive systems is proposed for the analysis and synthesis of fixed and adaptive controllers for robot manipulators. This approach clarifies the rationale behind the various fixed and adaptive control laws synthesized using Lyapunov functions.>

The model reference adaptive control of a two axis direct drive manipulator arm is presented. The two axes exhibit a significant dynamic interaction. The model reference adaptive controller is utilized in the velocity loop to adaptively decouple the dynamic interaction and to linearize the dynamics. The outer loop controller for positioning and tracking is designed based on the linear decoupled dynamics. The adaptive velocity loop controller as well as position loop controller are implemented digitally. The use of a series-parallel, as well as a parallel reference model is suggested in the adaptive velocity loop controller. The stability problems arising from the straightforward digital implementation of the continuous time algorithm are analyzed and a modification in the digital algorithm is introduced which guarantees the asymptotic stability of the system. Simulation and experimental results show a consistently superior performance of the manipulator under adaptive control.

The stability analysis of an adaptive control scheme for robotic manipulators, originally introduced by Horowitz and Tomizuka (1980), is presented in this paper. In the previous stability proof it was assumed that the manipulator parameter variation is negligible compared with the speed of adaptation. It is shown that this key assumption can be removed by introducing two modifications in the adaptive control scheme: 1. Reparametrizing the nonlinear terms in dynamic equations as linear functions of unknown but constant terms. 2. Defining the Coriolis compensation term in the control law as a bilinear function of the manipulator and model reference joint velocities, instead of a quadratic function of the manipulator joint velocities. The modified adaptive control scheme is shown to be globally asymptotically stable.