ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-based Nonlinear Robotic Systems

Koopman operator theory has been gaining momentum for model extraction, planning, and control of data-driven robotic systems. The Koopman operator's ability to extract dynamics from data depends heavily on the selection of an appropriate dictionary of lifting functions. In this paper we propose ACD-EDMD, a new method for Analytical Construction of Dictionaries of appropriate lifting functions for a range of data-driven Koopman operator based nonlinear robotic systems. The key insight of this work is that information about fundamental topological spaces of the nonlinear system (such as its configuration space and workspace) can be exploited to steer the construction of Hermite polynomial-based lifting functions. We show that the proposed method leads to dictionaries that are simple to implement while enjoying provable completeness and convergence guarantees when observables are weighted bounded. We evaluate ACD-EDMD using a range of diverse nonlinear robotic systems in both simulated and physical hardware experimentation (a wheeled mobile robot, a two-revolute-joint robotic arm, and a soft robotic leg). Results reveal that our method leads to dictionaries that enable high-accuracy prediction and that can generalize to diverse validation sets. The associated GitHub repository of our algorithm can be accessed at \url{https://github.com/UCR-Robotics/ACD-EDMD}.

Modeling and Trajectory Optimization for Standing Long Jumping of a Quadruped with A Preloaded Elastic Prismatic Spine

This paper presents a novel methodology to model and optimize trajectories of a quadrupedal robot with spinal compliance to improve standing jump performance compared to quadrupeds with a rigid spine. We introduce an elastic model for a prismatic robotic spine that is actively preloaded and mechanically lock-enabled at initial and maximum length, and develop a constrained trajectory optimization method to co-optimize the elastic parameters and motion trajectories toward enhanced jumping distance. Results reveal that a less stiff spring is likely to facilitate jumping performance not as a direct propelling source but as a means to unleash more motor power for propelling by trading-off overall energy efficiency. We also visualize the impact of spring coefficients on the overall optimization routine from energetic perspectives to identify the suitable parameter region.

Deformation Recovery Control and Post-Impact Trajectory Replanning for Collision-Resilient Mobile Robots

The paper focuses on collision-inclusive motion planning for impact-resilient mobile robots. We propose a new deformation recovery and replanning strategy to handle collisions that may occur at run-time. Contrary to collision avoidance methods that generate trajectories only in conservative local space or require collision checking that has high computational cost, our method directly generates (local) trajectories with imposing only waypoint constraints. If a collision occurs, our method then estimates the post-impact state and computes from there an intermediate waypoint to recover from the collision. To achieve so, we develop two novel components: 1) a deformation recovery controller that optimizes the robot's states during post-impact recovery phase, and 2) a post-impact trajectory replanner that adjusts the next waypoint with the information from the collision for the robot to pass through and generates a polynomial-based minimum effort trajectory. The proposed strategy is evaluated experimentally with an omni-directional impact-resilient wheeled robot. The robot is designed in house, and it can perceive collisions with the aid of Hall effect sensors embodied between the robot's main chassis and a surrounding deflection ring-like structure.

Position Control and Variable-Height Trajectory Tracking of a Soft Pneumatic Legged Robot

Soft pneumatic legged robots show promise in their ability to traverse a range of different types of terrain, including natural unstructured terrain met in applications like precision agriculture. They can adapt their body morphology to the intricacies of the terrain at hand, thus enabling robust and resilient locomotion. In this paper we capitalize upon recent developments on soft pneumatic legged robots to introduce a closed-loop trajectory tracking control scheme for operation over flat ground. Closed-loop pneumatic actuation feedback is achieved via a compact and portable pneumatic regulation board. Experimental results reveal that our soft legged robot can precisely control its body height and orientation while in quasi-static operation based on a geometric model. The robot can track both straight line and curved trajectories as well as variable-height trajectories. This work lays the basis to enable autonomous navigation for soft legged robots.

A Portable Agricultural Robot for Continuous Apparent Soil ElectricalConductivity Measurements to Improve Irrigation Practices

Near-ground sensing data, such as geospatial measurements of soil apparent electrical conductivity (ECa), are used in precision agriculture to improve farming practices and increase crop yield. Near-ground sensors provide valuable information, yet, the process of collecting, assessing, and interpreting measurements requires significant human labor. Automating parts of this process via the use of mobile robots can help decrease labor burden, and increase the accuracy and frequency of data collections, and overall increase the adoption and use of ECa measurement technology. This paper introduces a roboticized means to autonomously perform geospatial ECa measurements and map soil moisture content in micro-irrigated orchard systems. We retrofit a small wheeled mobile robot with a small electromagnetic induction sensor by studying and taking into consideration the effect of the robot body to the sensor's readings, and develop a software stack to enable autonomous logging of geo-referenced measurements. The proposed roboticized ECa measurement method is evaluated by mapping a 50m x 30m field against the baseline of human-conducted measurements obtained by walking the sensor in the same field and following the same path. Experimental testing reveals that our approach yields roboticized measurements comparable to human-conducted ones, despite the robot's small form factor.

Enhancement for Robustness of Koopman Operator-based Data-driven Mobile Robotic Systems

Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. Despite its widespread use, research on safety guarantees for systems the dynamics of which are extracted via the Koopman operator, has started receiving attention only recently. In this paper, we propose a way to quantify the prediction error because of noisy measurements when the Koopman operator is approximated via Extended Dynamic Mode Decomposition. We further develop an enhanced robot control strategy to endow robustness to a class of data-driven (robotic) systems that rely on Koopman operator theory, and we show how part of the strategy can happen offline in an effort to make our algorithm capable of real-time implementation. We perform a parametric study to evaluate the (theoretical) performance of the algorithm using a Van der Pol oscillator, and conduct a series of simulated experiments in Gazebo using a non-holonomic wheeled robot.

Task Planning on Stochastic Aisle Graphs for Precision Agriculture

This work addresses task planning under uncertainty for precision agriculture applications whereby task costs are uncertain and the gain of completing a task is proportional to resource consumption (such as water consumption in precision irrigation). The goal is to complete all tasks while prioritizing those that are more urgent, and subject to diverse budget thresholds and stochastic costs for tasks. To describe agriculture-related environments that incorporate stochastic costs to complete tasks, a new Stochastic-Vertex-Cost Aisle Graph (SAG) is introduced. Then, a task allocation algorithm, termed Next-Best-Action Planning (NBA-P), is proposed. NBA-P utilizes the underlying structure enabled by SAG, and tackles the task planning problem by simultaneously determining the optimal tasks to perform and an optimal time to exit (i.e. return to a base station), at run-time. The proposed approach is tested with both simulated data and real-world experimental datasets collected in a commercial vineyard, in both single- and multi-robot scenarios. In all cases, NBA-P outperforms other evaluated methods in terms of return per visited vertex, wasted resources resulting from aborted tasks (i.e. when a budget threshold is exceeded), and total visited vertices.

Toward Impact-resilient Quadrotor Design, Collision Characterization and Recovery Control to Sustain Flight after Collisions

Collision detection and recovery for aerial robots remain a challenge because of the limited space for sensors and local stability of the flight controller. We introduce a novel collision-resilient quadrotor that features a compliant arm design to enable free flight while allowing for one passive degree of freedom to absorb shocks. We further propose a novel collision detection and characterization method based on Hall sensors, as well as a new recovery control method to generate and track a smooth trajectory after a collision occurs. Experimental results demonstrate that the robot can detect and recover from high-speed collisions with various obstacles such as walls and poles. Moreover, it can survive collisions that are hard to detect with existing methods based on IMU data and contact models, for example, when colliding with unstructured surfaces, or being hit by a moving obstacle while hovering.

Motion Planning for Collision-resilient Mobile Robots in Obstacle-cluttered Unknown Environments with Risk Reward Trade-offs

Collision avoidance in unknown obstacle-cluttered environments may not always be feasible. This paper focuses on an emerging paradigm shift in which potential collisions with the environment can be harnessed instead of being avoided altogether. To this end, we introduce a new sampling-based online planning algorithm that can explicitly handle the risk of colliding with the environment and can switch between collision avoidance and collision exploitation. Central to the planner's capabilities is a novel joint optimization function that evaluates the effect of possible collisions using a reflection model. This way, the planner can make deliberate decisions to collide with the environment if such collision is expected to help the robot make progress toward its goal. To make the algorithm online, we present a state expansion pruning technique that significantly reduces the search space while ensuring completeness. The proposed algorithm is evaluated experimentally with a built-in-house holonomic wheeled robot that can withstand collisions. We perform an extensive parametric study to investigate trade-offs between (user-tuned) levels of risk, deliberate collision decision making, and trajectory statistics such as time to reach the goal and path length.

Development and Testing of a Novel Automated Insect Capture Module for Sample Collection and Transfer

There exists an urgent need for efficient tools in disease surveillance to help model and predict the spread of disease. The transmission of insect-borne diseases poses a serious concern to public health officials and the medical and research community at large. In the modeling of this spread, we face bottlenecks in (1) the frequency at which we are able to sample insect vectors in environments that are prone to propagating disease, (2) manual labor needed to set up and retrieve surveillance devices like traps, and (3) the return time in analyzing insect samples and determining if an infectious disease is spreading in a region. To help address these bottlenecks, we present in this paper the design, fabrication, and testing of a novel automated insect capture module (ICM) or trap that aims to improve the rate of transferring samples collected from the environment via aerial robots. The ICM features an ultraviolet light attractant, passive capture mechanism, panels which can open and close for access to insects, and a small onboard computer for automated operation and data logging. At the same time, the ICM is designed to be accessible; it is small-scale, lightweight and low-cost, and can be integrated with commercially available aerial robots. Indoor and outdoor experimentation validates ICM's feasibility in insect capturing and safe transportation. The device can help bring us one step closer toward achieving fully autonomous and scalable epidemiology by leveraging autonomous robots technology to aid the medical and research community.