Soft robots can execute tasks with safer interactions. However, control techniques that can effectively exploit the systems' capabilities are still missing. Differential dynamic programming (DDP) has emerged as a promising tool for achieving highly dynamic tasks. But most of the literature deals with applying DDP to articulated soft robots by using numerical differentiation, in addition to using pure feed-forward control to perform explosive tasks. Further, underactuated compliant robots are known to be difficult to control and the use of DDP-based algorithms to control them is not yet addressed. We propose an efficient DDP-based algorithm for trajectory optimization of articulated soft robots that can optimize the state trajectory, input torques, and stiffness profile. We provide an efficient method to compute the forward dynamics and the analytical derivatives of series elastic actuators (SEA)/variable stiffness actuators (VSA) and underactuated compliant robots. We present a state-feedback controller that uses locally optimal feedback policies obtained from DDP. We show through simulations and experiments that the use of feedback is crucial in improving the performance and stabilization properties of various tasks. We also show that the proposed method can be used to plan and control underactuated compliant robots, with varying degrees of underactuation effectively.
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We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we can formulate diffusion-based generative modeling as a minimization of the Kullback-Leibler divergence between suitable measures in path space. Finally, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences. We demonstrate that our time-reversed diffusion sampler (DIS) can outperform other diffusion-based sampling approaches on multiple numerical examples.
Flexible robots have advantages over rigid robots in their ability to conform physically to their environment and to form a wide variety of shapes. Sensing the force applied by or to flexible robots is useful for both navigation and manipulation tasks, but it is challenging due to the need for the sensors to withstand the robots' shape change without encumbering their functionality. Also, for robots with long or large bodies, the number of sensors required to cover the entire surface area of the robot body can be prohibitive due to high cost and complexity. We present a novel soft air pocket force sensor that is highly flexible, lightweight, relatively inexpensive, and easily scalable to various sizes. Our sensor produces a change in internal pressure that is linear with the applied force. We present results of experimental testing of how uncontrollable factors (contact location and contact area) and controllable factors (initial internal pressure, thickness, size, and number of interior seals) affect the sensitivity. We demonstrate our sensor applied to a vine robot-a soft inflatable robot that "grows" from the tip via eversion-and we show that the robot can successfully grow and steer towards an object with which it senses contact.
A Data-Driven Approach to Synthesizing Dynamics-Aware Trajectories for Underactuated Robotic Systems
We consider joint trajectory generation and tracking control for under-actuated robotic systems. A common solution is to use a layered control architecture, where the top layer uses a simplified model of system dynamics for trajectory generation, and the low layer ensures approximate tracking of this trajectory via feedback control. While such layered control architectures are standard and work well in practice, selecting the simplified model used for trajectory generation typically relies on engineering intuition and experience. In this paper, we propose an alternative data-driven approach to dynamics-aware trajectory generation. We show that a suitable augmented Lagrangian reformulation of a global nonlinear optimal control problem results in a layered decomposition of the overall problem into trajectory planning and feedback control layers. Crucially, the resulting trajectory optimization is dynamics-aware, in that, it is modified with a tracking penalty regularizer encoding the dynamic feasibility of the generated trajectory. We show that this tracking penalty regularizer can be learned from system rollouts for independently-designed low layer feedback control policies, and instantiate our framework in the context of a unicycle and a quadrotor control problem in simulation. Further, we show that our approach handles the sim-to-real gap through experiments on the quadrotor hardware platform without any additional training. For both the synthetic unicycle example and the quadrotor system, our framework shows significant improvements in both computation time and dynamic feasibility in simulation and hardware experiments.
We study distributed estimation and learning problems in a networked environment in which agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. By exchanging information about their private observations, the agents can collectively estimate the unknown quantities, but they also face privacy risks. The goal of our aggregation schemes is to combine the observed data efficiently over time and across the network, while accommodating the privacy needs of the agents and without any coordination beyond their local neighborhoods. Our algorithms enable the participating agents to estimate a complete sufficient statistic from private signals that are acquired offline or online over time, and to preserve the privacy of their signals and network neighborhoods. This is achieved through linear aggregation schemes with adjusted randomization schemes that add noise to the exchanged estimates subject to differential privacy (DP) constraints. In every case, we demonstrate the efficiency of our algorithms by proving convergence to the estimators of a hypothetical, omniscient observer that has central access to all of the signals. We also provide convergence rate analysis and finite-time performance guarantees and show that the noise that minimizes the convergence time to the best estimates is the Laplace noise, with parameters corresponding to each agent's sensitivity to their signal and network characteristics. Finally, to supplement and validate our theoretical results, we run experiments on real-world data from the US Power Grid Network and electric consumption data from German Households to estimate the average power consumption of power stations and households under all privacy regimes.
Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.
Software Engineering is an applied discipline and concepts are difficult to grasp only at a theoretical level alone. In the context of a project management course, we introduced and evaluated the use of software process simulation (SPS) based games for improving students' understanding of software development processes. The effects of the intervention were measured by evaluating the students' arguments for choosing a particular development process. The arguments were assessed with the Evidence-Based Reasoning framework, which was extended to assess the strength of an argument. The results indicate that students generally have difficulty providing strong arguments for their choice of process models. Nevertheless, the assessment indicates that the intervention of the SPS game had a positive impact on the students' arguments. Even though the illustrated argument assessment approach can be used to provide formative feedback to students, its use is rather costly and cannot be considered a replacement for traditional assessments.
The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the computation to make it real-time. In this paper, we propose a learning-based approach to obtain a compact but sufficiently rich mechanical representation. Our choice is based on nonlinear compliance data in the actuator/effector space provided by a condensation of the FEM model. We demonstrate that this compact model can be learned with a reasonable amount of data and, at the same time, be very efficient in terms of modeling, since we can deduce the direct and inverse kinematics of the robot. We also show how to couple some models learned individually in particular on an example of a gripper composed of two soft fingers. Other results are shown by comparing the inverse model derived from the full FEM model and the one from the compact learned version. This work opens new perspectives, namely for the embedded control of soft robots, but also for their design. These perspectives are also discussed in the paper.
Accurate error estimation is crucial in model order reduction, both to obtain small reduced-order models and to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation approaches, knowledge about the time integration scheme is mandatory, e.g., the residual-based error estimators proposed for the reduced basis method. This poses a challenge when automatic ordinary differential equation solver libraries are used to perform the time integration. To address this, we present a data-enhanced approach for a posteriori error estimation. Our new formulation enables residual-based error estimators to be independent of any time integration method. To achieve this, we introduce a corrected reduced-order model which takes into account a data-driven closure term for improved accuracy. The closure term, subject to mild assumptions, is related to the local truncation error of the corresponding time integration scheme. We propose efficient computational schemes for approximating the closure term, at the cost of a modest amount of training data. Furthermore, the new error estimator is incorporated within a greedy process to obtain parametric reduced-order models. Numerical results on three different systems show the accuracy of the proposed error estimation approach and its ability to produce ROMs that generalize well.
Many food products involve mixtures of ingredients, where the mixtures can be expressed as combinations of ingredient proportions. In many cases, the quality and the consumer preference may also depend on the way in which the mixtures are processed. The processing is generally defined by the settings of one or more process variables. Experimental designs studying the joint impact of the mixture ingredient proportions and the settings of the process variables are called mixture-process variable experiments. In this article, we show how to combine mixture-process variable experiments and discrete choice experiments, to quantify and model consumer preferences for food products that can be viewed as processed mixtures. First, we describe the modeling of data from such combined experiments. Next, we describe how to generate D- and I-optimal designs for choice experiments involving mixtures and process variables, and we compare the two kinds of designs using two examples.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
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