Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.

This paper presents an optimization-based motion planning methodology for snake robots operating in constrained environments. By using a reduced-order model, the proposed approach simplifies the planning process, enabling the optimizer to autonomously generate gaits while constraining the robot's footprint within tight spaces. The method is validated through high-fidelity simulations that accurately model contact dynamics and the robot's motion. Key locomotion strategies are identified and further demonstrated through hardware experiments, including successful navigation through narrow corridors.

Accurate estimation of aerodynamic forces is essential for advancing the control, modeling, and design of flapping-wing aerial robots with dynamic morphing capabilities. In this paper, we investigate two distinct methodologies for force estimation on Aerobat, a bio-inspired flapping-wing platform designed to emulate the inertial and aerodynamic behaviors observed in bat flight. Our goal is to quantify aerodynamic force contributions during tethered flight, a crucial step toward closed-loop flight control. The first method is a physics-based observer derived from Hamiltonian mechanics that leverages the concept of conjugate momentum to infer external aerodynamic forces acting on the robot. This observer builds on the system’s reduced-order dynamic model and utilizes real-time sensor data to estimate forces without requiring training data. The second method employs a neural network-based regression model, specifically a multi-layer perceptron (MLP), to learn a mapping from joint kinematics, flapping frequency, and environmental parameters to aerodynamic force outputs. We evaluate both estimators using a 6-axis load cell in a high-frequency data acquisition setup that enables fine-grained force measurements during periodic wingbeats. The conjugate momentum observer and the regression model demonstrate strong agreement across three force components (Fx, Fy, Fz).

This paper presents the development and integration of a vision-guided loco-manipulation pipeline for Northeastern University’s snake robot, COBRA. The system leverages a YOLOv8-based object detection model and depth data from an onboard stereo camera to estimate the 6-DOF pose of target objects in real time. We introduce a framework for autonomous detection and control, enabling closed-loop loco-manipulation for transporting objects to specified goal locations. Additionally, we demonstrate open-loop experiments in which COBRA successfully performs real-time object detection and loco-manipulation tasks.

Contact-rich problems, such as snake robot locomotion, offer unexplored yet rich opportunities for optimization-based trajectory and acyclic contact planning. So far, a substantial body of control research has focused on emulating snake locomotion and replicating its distinctive movement patterns using shape functions that either ignore the complexity of interactions or focus on complex interactions with matter (e.g., burrowing movements). However, models and control frameworks that lie in between these two paradigms and are based on simple, fundamental rigid body dynamics, which alleviate the challenging contact and control allocation problems in snake locomotion, remain absent. This work makes meaningful contributions, substantiated by simulations and experiments, in the following directions: 1) introducing a reduced-order model based on Moreau’s stepping-forward approach from differential inclusion mathematics, 2) verifying model accuracy, 3) experimental validation.

Multi-modal ground-aerial robots have been extensively studied, with a significant challenge lying in the integration of conflicting requirements across different modes of operation. The Husky robot family, developed at North-eastern University, and specifically the Husky v.2 discussed in this study, addresses this challenge by incorporating posture manipulation and thrust vectoring into multi-modal locomotion through structure repurposing. This quadrupedal robot features leg structures that can be repurposed for dynamic legged locomotion and flight. In this paper, we present the hardware design of the robot and report primary results on dynamic quadrupedal legged locomotion and hovering.

Husky Carbon, a robot developed by Northeastern University, serves as a research platform to explore unification of posture manipulation and thrust vectoring. Unlike conventional quadrupeds, its joint actuators and thrusters enable enhanced control authority, facilitating thruster-assisted narrow-path walking. While a unified Model Predictive Control (MPC) framework optimizing both ground reaction forces and thruster forces could theoretically address this control problem, its feasibility is limited by the low torque-control bandwidth of the system’s lightweight actuators. To overcome this challenge, we propose a decoupled control architecture: a Raibert-type controller governs legged locomotion using position-based control, while an MPC regulates the thrusters augmented by learned Contact Residual Dynamics (CRD) to account for leg-ground impacts. This separation bypasses the torque-control rate bottleneck while retaining the thruster MPC to explicitly account for leg-ground impact dynamics through learned residuals. We validate this approach through both simulation and hardware experiments, showing that the decoupled control architecture with CRD performs more stable behavior in terms of push recovery and cat-like walking gait compared to the decoupled controller without CRD.

Along with the advancement of robot skin technology, there has been notable progress in the development of snake robots featuring body-surface tactile perception. In this study, we proposed a locomotion control framework for snake robots that integrates tactile perception to augment their adaptability to various terrains. Our approach embraces a hierarchical reinforcement learning (HRL) architecture, wherein the high-level orchestrates global navigation strategies while the low-level uses curriculum learning for local navigation maneuvers. Due to the significant computational demands of collision detection in whole-body tactile sensing, the efficiency of the simulator is severely compromised. Thus a distributed training pattern to mitigate the efficiency reduction was adopted. We evaluated the navigation performance of the snake robot in complex large-scale cave exploration with challenging terrains to exhibit improvements in motion efficiency, evidencing the efficacy of tactile perception in terrain-adaptive locomotion.

Robot designs can take many inspirations from nature, where there are many examples of highly resilient and fault-tolerant locomotion strategies to navigate complex terrains by using multi-functional appendages. For example, Chukar and Hoatzin birds can repurpose their wings for quadrupedal walking and wing-assisted incline running (WAIR) to climb steep surfaces. We took inspiration from nature and designed a morphing robot with multi-functional thruster-wheel appendages that allows the robot to change its mode of locomotion by transforming into a rover, quad-rotor, mobile inverted pendulum (MIP), and other modes. In this work, we derive a dynamic model and formulate a nonlinear model predictive controller to perform WAIR to showcase the unique capabilities of our robot. We implemented the model and controller in a numerical simulation and experiments to show their feasibility and the capabilities of our transforming multimodal robot.

Object manipulation has been extensively studied in the context of fixed base and mobile manipulators. However, the overactuated locomotion modality employed by snake robots allows for a unique blend of object manipulation through locomotion, referred to as loco-manipulation. The following work presents an optimization approach to solving the loco-manipulation problem based on non-impulsive implicit contact path planning for our snake robot COBRA. We present the mathematical framework and show high-fidelity simulation results and experiments to demonstrate the effectiveness of our approach.

Passive tumbling structures are energy efficient, but often sacrifice control authority due to their under actuated nature. Unlike many passive tumbling robots, Northeastern University’s COBRA is a snake robot with eleven articulated joints that transforms into a wheel-like structure with a high degree of posture control during tumbling, and using this posture manipulation, COBRA can control its forward velocity and heading angle while tumbling. This paper presents a mathematical framework that describes the dynamics of posture manipulation during tumbling and identifies two types of control actions that allow it to control its movement. This is validated in hardware testing to demonstrate obstacle avoidance during passive tumbling using only posture manipulation.

Investigations of unmanned aerial vehicles (UAV s) for planetary exploration and payload manipulation have become a strong focus of research within space robotics. Among possible solutions, balloon-based systems possess merits that make them extremely attractive, such as their simple operation mechanism and endured operation time. However, there are many hurdles to overcome to achieve robust trajectory tracking performance for balloon-based applications. In this work, in order to facilitate the control and versatile use of balloons for near-surface planetary payload manipulation, a novel robotic platform and control strategy featuring the coordinated servoing of multiple unmanned ground vehicles (UGVs) to actuate a cable-driven balloon and the suspended payload is proposed. An earthbound prototype and dynamic model of this system are designed to allow for the investigation of payload trajectory tracking performance using a tailored Model Predictive Controller in simulation and experiment.

This work briefly covers our efforts to stabilize the flight dynamics of Northeatern's tailless bat-inspired micro aerial vehicle, Aerobat. Flapping robots are not new. A plethora of examples is mainly dominated by insect-style design paradigms that are passively stable. However, Aerobat, in addition for being tailless, possesses morphing wings that add to the inherent complexity of flight control. The robot can dynamically adjust its wing platform configurations during gaitcycles, increasing its efficiency and agility. We employ a guard design with manifold small thrusters to stabilize Aerobat's position and orientation in hovering, a flapping system in tandem with a multi-rotor. For flight control purposes, we take an approach based on assuming the guard cannot observe Aeroat's states. Then, we propose an observer to estimate the unknown states of the guard which are then used for closed-loop hovering control of the Guard-Aerobat platform.

Some animals exhibit multi-modal locomotion capability to traverse a wide range of terrains and environments, such as amphibians that can swim and walk or birds that can fly and walk. This capability is extremely beneficial for expanding the animal's habitat range and they can choose the most energy efficient mode of locomotion in a given environment. The robotic biomimicry of this multi-modal locomotion capability can be very challenging but offer the same advantages. However, the expanded range of locomotion also increases the complexity of performing localization and path planning. In this work, we present our morphing multi-modal robot, which is capable of ground and aerial locomotion, and the implementation of readily available SLAM and path planning solutions to navigate a complex indoor environment.

Flying animals possess highly complex physical characteristics and are capable of performing agile maneuvers using their wings. The flapping wings generate complex wake structures that influence the aerodynamic forces, which can be difficult to model. While it is possible to model these forces using fluidstructure interaction, it is very computationally expensive and difficult to formulate. In this paper, we follow a simpler approach by deriving the aerodynamic forces using a relatively small number of states and presenting them in a simple state-space form. The formulation utilizes Prandtl's lifting line theory and Wagner's function to determine the unsteady aerodynamic forces acting on the wing in a simulation, which then are compared to experimental data of the bat-inspired robot called the Aerobat. The simulated trailingedge vortex shedding can be evaluated from this model, which then can be analyzed for a wake-based gait design approach to improve the aerodynamic performance of the robot.

We report the design of a morpho-functional robot called Husky Carbon. Our goal is to integrate two forms of mobility, aerial and quadrupedal legged locomotion, within a single platform. There are prohibitive design restrictions such as tight power budget and payload, which can particularly become important in aerial flights. To address these challenges, we pose a problem called the Mobility Value of Added Mass (MVAM) problem. In the MVAM problem, we attempt to allocate mass in our designs such that the energetic performance is affected the least. To solve the MVAM problem, we adopted a generative design approach using Grasshopper’s evolutionary solver to synthesize a parametric design space for Husky. Then, this space was searched for the morphologies that could yield a minimized Total Cost Of Transport (TCOT) and payload. This approach revealed that a front heavy quadrupedal robot can achieve a lower TCOT while retaining larger margins on allowable added mass to its design. Based on this framework Husky was built and tested as a front heavy robot.

The flight characteristics of bats remarkably have been overlooked in aerial drone designs. Unlike other animals, bats leverage the manipulation of inertial dynamics to exhibit aerial flip turns when they perch. Inspired by this unique maneuver, this work develops and uses a tiny robot called Harpoon to demonstrate that the preparation for upside-down landing is possible through: 1) reorientation towards the landing surface through zero-angular-momentum turns and 2) reaching to the surface through shooting a detachable landing gear. The closed-loop manipulations of inertial dynamics takes place based on a symplectic description of the dynamical system (body and appendage), which is known to exhibit an excellent geometric conservation properties.

Planning flight trajectories is important for practical application of flying systems. This topic has been well studied for fixed and rotary winged aerial vehicles, but far fewer works have explored it for flapping systems. Bat Bot (B2) is a bio-inspired flying robot that mimics bat flight, and it possesses the ability to follow a designed trajectory with its on-board electronics and sensing. However, B2's periodic flapping and its complex aerodynamics present major challenges in modeling and planning feasible flight paths. In this paper, we present a generalized approach that uses a model with direct collocation methods to plan dynamically feasible flight maneuvers. The model is made to be both accurate through collection of load cell force data for parameter selection and computationally inexpensive such that it can be used efficiently in a nonlinear solver. We compute the trajectory of launching B2 to a desired altitude and a banked turn maneuver, and we validate our methods with experimental flight results of tracking the launch trajectory with a PD controller.

Bats are unique in that they can achieve unrivaled agile maneuvers due to their functionally versatile wing conformations. Among these maneuvers, roosting (landing) has captured attentions because bats perform this acrobatic maneuver with a great composure. This work attempts to reconstruct bat landing maneuvers with a Micro Aerial Vehicle (MAV) called Allice. Allice is capable of adjusting the position of its Center of Gravity (CG) with respect to the Center of Pressure (CP) using a nonlinear closed-loop feedback. This nonlinear control law, which is based on the method of input-output feedback linearization, enables attitude regulations through variations in CG-CP distance. To design the model-based nonlinear controller, the Newton-Euler dynamic model of the robot is considered, in which the aerodynamic coefficients of lift and drag are obtained experimentally. The performance of the proposed control architecture is validated by conducting several experiments.

It is challenging to analyze the aerial locomotion of bats because of the complicated and intricate relationship between their morphology and flight capabilities. Developing a biologically inspired bat robot would yield insight into how bats control their body attitude and position through the complex interaction of nonlinear forces (e.g., aerodynamic) and their intricate musculoskeletal mechanism. The current work introduces a biologically inspired soft robot called Bat Bot (B2). The overall system is a flapping machine with 5 Degrees of Actuation (DoA). This work reports on some of the preliminary untethered flights of B2. B2 has a nontrivial morphology and it has been designed after examining several biological bats. Key DoAs, which contribute significantly to bat flight, are picked and incorporated in B2's flight mechanism design. These DoAs are: 1) forelimb flapping motion, 2) forelimb mediolateral motion (folding and unfolding) and 3) hindlimb dorsoventral motion (upward and downward movement).

This paper presents a systematic flight controller design based on the mathematics of parametrized manifolds and calculus of variations for the Bat Bot (B2), which possesses many articulated wings. Wing kinematics and morphological properties are crucial in the powered flight of flying vertebrates. The articulated skeleton of these mammals, which contains many degrees of actuation and underactuation, has made it difficult to understand the connection between the bat's flight dynamics and its intricate array of physiological and morphological specializations. B2 is a biomimetic micro aerial vehicle (MAV) that possesses similar morphological properties to a bat in order to duplicate bats powered ballistic motion. In an effort to design the advanced flight control algorithm for B2, this paper reports two major contributions. First, a systematic mathematical framework is introduced that evaluates the holonomically-constrained Lagrangian model of a flapping robot with specified active and passive degrees of freedom (DoF) in order to locate physically feasible and biologically meaningful periodic solutions using optimization. These are parametrized constraint manifolds; the flapping wing dynamics are governed by these manifolds. Second, calculus of variations and the well-recognized method of inverse dynamics are applied in order to synthesize the flight control algorithm for the flapping wings.

This paper reports on an underactuated 3D bipedal robot with passive feet that can start from a quiet standing position, initiate a walking gait, and traverse the length of the laboratory (approximately 10 m) at a speed of roughly 1 m/s. The controller was developed using the method of virtual constraints, a control design method first used on the planar point-feet robots Rabbit and MABEL. For the preliminary experiments reported here, virtual constraints were experimentally tuned to achieve robust planar walking and then 3D walking. A key feature of the controller leading to successful 3D walking is the particular choice of virtual constraints in the lateral plane, which implement a lateral balance control strategy similar to SIMBICON. To our knowledge, MARLO is the most highly underactuated bipedal robot to walk unassisted in 3D.

This paper presents a feedback controller that allows MABEL, which is a kneed planar bipedal robot with 1-m-long legs, to accommodate terrain that presents large unexpected increases and decreases in height. The robot is provided no information regarding where the change in terrain height occurs and by how much. A finite-state machine is designed that manages transitions among controllers for flat-ground walking, stepping-up and -down, and a trip reflex. If the robot completes a step, the depth of a step-down or the height of a step-up can be immediately estimated at impact from the lengths of the legs and the angles of the robot’s joints. The change in height can be used to invoke a proper control response. On the other hand, if the swing leg impacts an obstacle during a step, or has a premature impact with the ground, a trip reflex is triggered on the basis of specially designed contact switches on the robot’s shins, contact switches at the end of each leg, and the current configuration of the robot. The design of each control mode and the transition conditions among them are presented. This paper concludes with experimental results of MABEL (blindly) accommodating various types of platforms, including ascent of a 12.5-cm-high platform, stepping-off an 18.5-cm-high platform, and walking over a platform with multiple ascending and descending steps.

This paper presents a feedback controller that allows MABEL, a kneed, planar bipedal robot, with 1 m-long legs, to accommodate an abrupt 20 cm decrease in ground height. The robot is provided information on neither where the step down occurs, nor by how much. After the robot has stepped off a raised platform, however, the height of the platform can be estimated from the lengths of the legs and the angles of the robot's joints. A real-time control strategy is implemented that uses this on-line estimate of step-down height to switch from a baseline controller, that is designed for flat-ground walking, to a second controller, that is designed to attenuate torso oscillation resulting from the step-down disturbance. After one step, the baseline controller is re-applied. The control strategy is developed on a simplified-design model of the robot and then verified on a more realistic model before being evaluated experimentally. The paper concludes with experimental results showing MABEL (blindly) stepping off a 20 cm high platform.