Joo H. Kim

Incorporating phase transitions such as impulsive or non-impulsive contact interactions and subtasks into trajectory planning is a critical but challenging problem for robot control. This study introduces a unified, derivative-based, direct collocation framework with conditional constraints of general tasks and mathematical forms for optimal robot trajectories and phase transitions, without the need for the pre-specified sequence/timing, explicit contact forces, complementarity constraints, multi-level solvers, or additional variables/constraints present in most contact-implicit or logic-geometric schemes. Encoded conditions detect or plan the phase transitions and transform the relevant constraint bounds, which are equivalent to the equality/inequality form, tightening/relaxation, or addition/removal of the constraints. The formulations are embedded in a sequential quadratic programming algorithm, with the allowance of outer loops for hybrid dynamic systems, where the numerical convergence of the solution toward optimality is confirmed by iteration and sensitivity analyses. The framework is validated and demonstrated for three example tasks with distinct contact phases and boundary nonlinearities—bouncing ball, manipulation, and legged balancing with tipping—with different levels of system actuation (unactuated, under-actuated, and fully-actuated) in non-redundant problems for prediction and redundant problems for optimization.

Energy expenditure (EE) estimation during walking has significant applications in healthcare, sports science, and rehabilitation, but remains challenging to measure in real-world settings. Existing wearable approaches often require complex multi-sensor systems or extensive training datasets, limiting their practical implementation. We propose a biomechanically-informed machine learning approach to estimate EE during walking in healthy subjects, based on sagittal joint powers of the body segment, derived from a single sacrum-mounted inertial measurement unit (IMU). Segmental analysis confirmed that the stance-leg joint mechanical power exhibits the strong correlation with whole-body EE. Scaling relationships between efficiency-weighted segmental joint mechanical power and whole-body EE were first established by regression analysis. Segmental analysis revealed that sagittal-plane joint mechanical power of the body segment, particularly the stance leg strongly correlates with whole-body joint mechanical power (R > 0.9 across subjects and walking speeds). Leveraging this relationship and a lightweight artificial neural network that predicts segmental joint dynamics from an IMU data, the whole-body EE was estimated from the stance-leg sagittal power with efficiency coefficients and the regression-based scale factor. The approach was validated in 13 healthy adults walking at multiple speeds on a treadmill, with ground-truth EE measured via indirect calorimetry. The results demonstrated remarkable consistency both within individuals across speeds and across different subjects (coefficient of variation < 2%), suggesting a robust biomechanical linkage. Furthermore, joint dynamics of the stance leg were accurately estimated from single sacrum-mounted IMU data incorporating a single-leg stance partition and gait speed information. The resulting stance-leg power estimates enabled accurate EE estimation (RMSE 0.69 W/kg) across an independent cohort. This study demonstrates that sagittal-plane joint mechanical power of the body segment particularly the stance leg serves as a reliable biomechanical surrogate for whole-body EE during walking, which can be robustly inferred through the efficiency-weighting and regression-scaling. The proposed method offers a simple and practical solution for wearable EE monitoring, with potential applications in clinical rehabilitation, exercise prescription, and daily health tracking.

Abstract Robust push recovery controllers must stabilize a system in response to various perturbations. Existing approaches often determine these actions based on reduced-order models, which can either underutilize the system's capabilities or lead to dynamic infeasibility. This study addresses this gap by integrating balanced state basins, computed from whole-body dynamics, into a partition-aware controller. These basins represent sets in center-of-mass state space, from which a robot with an idealized controller can achieve a desired equilibrium state, subject to contact requirements such as step length. The basins are constructed using an optimization framework that incorporates whole-body dynamics alongside system- and task-specific constraints. Polynomial regression is used to approximate the basin as a function of step length. The parameterized basins partition the state space into regions requiring a step and those that do not, serving as a decision boundary between the non-stepping and stepping strategies. The non-stepping sub-controller is designed to return the system to a static equilibrium without changing contact and uses an iterative linear quadratic regulator with a single-rigid-body-inspired model for efficient trajectory optimization. The stepping sub-controller models the system dynamics as a passive 3D pendulum and uses a capture-point-based planner to achieve a stabilizing step. The combined use of these sub-controllers and basin estimation enables multi-step balance recovery despite planning only one step at a time. Real-time simulations demonstrate the controller's potential to augment the computational efficiency of reduced-order models with the dynamic feasibility guarantees of full-order balanced state basins.

Abstract Energy-efficient walking is crucial for deploying bipedal robots due to their limited energy resources. Existing studies often focus on energy-efficient control strategies or predictive analyses of energy-informed gait transitions, such as from walking to running. However, the impact of the walking gait parameters and system characteristics, such as morphology and rotor inertia, on energy efficiency remains underexplored. This study addresses this gap by analyzing the energy-optimality of level-ground walking under variations in step length, step time, gait configuration, double-support phase ratio, and rotor inertia. An optimization framework is employed to compute the optimal energetics by incorporating the whole-body and hybrid dynamics of the robot and task-specific constraints. The energy-optimal curves are constructed by solving a series of constrained optimization problems, each based on a set of the desired step length, step time, pre-impact gait configuration, double-support phase duration, and rotor inertia. Rotor inertia is incorporated through a computationally efficient approximation embedded in the actuation constraints and the objective, circumventing the need to modify the dynamics formulation. The optimal predictions are then compared with simulated behavior from approximately straight-knee walking using a 3-D linear-inverted–pendulum-based walking controller. Analysis of the energy-optimal curves highlighted the detrimental effects of rotor inertia on energy efficiency while suggesting a complex relation with the maximum walking speed, a factor relevant to stability. Furthermore, comparing optimal predictions with the simulated data challenges the assumption that straight-knee walking is inherently energy-efficient, revealing a deeper interplay between gait mechanics and energy efficiency.

Objective: Current methods for measuring metabolic energy expenditure (MEE) constrain experiment design and only provide time-averaged values. We propose a novel two-stage predictive model using surrogate learners in the first stage for physiological dynamics and gradient-boosted regression trees in the second stage to learn a generalized representation of instantaneous, whole-body MEE. Methods: Kinematic, kinetic, metabolic, and surface electromyograph data were recorded for nine human subjects in level, over-ground walking at 100%, 70%, 85%, 115%, and 130% subject-preferred speeds. We use surrogate learners to encode fundamental information about the time-varying properties of MEE. A gradient-boosted machine-learning model was then trained on the surrogate functions’ outputs. For robustness, an information-theoretic data selection step was added during model training. The trained model uses joint torques and angular velocities to predict instantaneous, whole-body MEE during walking. Results: The model accurately predicts instantaneous MEE without subject-specific input parameters. Shapley Additive Explanations were used to investigate energetic features of the learned MEE function and demonstrate alignment with literature. We find similarities between the model’s MEE predictions, muscle mechanical work rate, and normal ground reaction forces, suggesting a link between MEE and the work required to raise the center of mass. Conclusion: The proposed approach provides an alternative to experimental MEE measurement while balancing the generalizability and complexity trade-off typically imposed on existing computational, predictive models. Significance: Evaluating MEE of human motion can provide insight into underlying biomechanics and inform clinical and engineering practices.

Abstract Maintaining stability in jumping robots remains a challenge due to their hybrid dynamics. Despite recent advances, existing research lacks a clear definition and comprehensive criteria for jumping stability. To address this gap, the definition of a post-landing stable state is presented and used to formulate state-space partitions, or post-landing stable state basins, that serve as general stability criteria for flight-to-stance tasks. A hybrid-phase approach is applied to solve the flight and stance phases as separate sub-problems through analytical and optimization-based methods, subject to nonlinear system dynamics, environmental contact constraints, and task requirements. Post-landing stable state basins are constructed for a monoped jumping robot, Salto-1P, for two tasks, targeted jumping and cat-like righting, to demonstrate the use of the basins as comprehensive criteria for jumping stability. The stance-phase sub-problem solution, or landing state basin, is analyzed to determine the effect of and identify safe sets of landing state variables for balance after landing. This basin is also validated against simulated controller-specific basins of attraction. The basins obtained reveal the relationships between stability, task requirements, initial state variables such as body orientation and velocity, and landing state variables such as body angle at landing.

The complexity of the control and operation is one of the roadblocks of widespread utilization of humanoid robots. In this study, we introduce a novel approach to humanoid robot control by leveraging a mixed reality (MR) interface for whole-body balancing and manipulation. This interface system uses an MR headset to track the operator's movement and provide the operator with useful visual information for the control. The robot mimics the operator's movement through a motion retargeting method based on linear scaling and inverse kinematics. The operator obtains visual access to the robot's perspective view augmented with fiducial detection and perceives the current stability of the robot by evaluating the robot's center-of-mass state in real-time against the precomputed balanced state basin. In experimental demonstrations, the operator successfully controlled the robot to grasp and lift an object without falling. The common issues in teleoperation with virtual reality headsets, motion sickness and unawareness of their surroundings, are reduced to a low level by using the MR headset with transparent glasses. This study demonstrates the potential of MR in teleoperation with a motion retargeting and stability monitoring method.

Despite the importance and prevalence of loco-manipulation tasks by humanoids, existing criteria and control methods for stability are mostly developed for unloaded legged gait. In this paper, the stability during lifting tasks is comprehensively analyzed to determine the role of the lifted object mass in balancing. The stability of a simple two-degree-of-freedom lifting model and a whole-body humanoid robot are evaluated by constructing their balanced state boundaries, which represent their specific capabilities in maintaining balance, through an optimization-based framework for varying combinations of object mass, joint torque limits, and base of support dimensions. Comparative analysis of the rate of change of the linear and centroidal angular momenta quantifies the nonlinear and nontrivial tradeoffs, i.e., contribution or obstruction, of the effects of the object mass on balancing. Overall, increasing the object mass enhances balance capability subject to the limiting factors of system kinematic and actuation limits, center of pressure within the base of support, friction cone, and unilateral normal contact forces between the feet and the ground.

Abstract Stability evaluation is a vital aspect of successful balance control and design for humanoid robots. While balance stability has been extensively explored for push recovery during legged locomotion tasks in response to perturbations, less effort has been devoted toward developing a similar understanding for lifting tasks. Lifting involves unique interactions between the robot and lifted object, whose mass can significantly alter the mass distribution of the loaded robot and the upper extremities, which are typically ignored in legged robot balance. In this study, the balance stability of a humanoid robot during a lifting task is evaluated with a partition-based approach in the augmented center-of-mass-state space. The balanced state boundary is computed through an optimization-based method that incorporates the loaded robot’s whole-body system properties, such as kinematic and actuation limits, with full-order nonlinear system dynamics in the sagittal plane subject to foot-ground contact interactions and lifting task requirements. The boundaries are constructed for different combinations of object masses and lifting trajectories obtained with a zero-moment point constraint-based pattern generator. Trends in the boundaries and comparisons among them are used to identify the effect of different loading conditions and task parameters on balance stability due to kinematic and actuation limits, linear and angular momenta regulation, and mass distribution.

Abstract For successful push recovery in response to perturbations, a humanoid robot must select an appropriate stabilizing action. Existing approaches are limited because they are often derived from reduced-order models that ignore system-specific aspects such as swing leg dynamics or kinematic and actuation limits. In this study, the formulation of capturability for whole-body humanoid robots is introduced as a partition-based approach in the augmented center-of-mass (COM)-state space. The 1-step capturable boundary is computed from an optimization-based method that incorporates whole-body system properties with full-order nonlinear system dynamics in the sagittal plane including contact interactions with the ground and conditions for achieving a complete stop after stepping. The 1-step capturable boundary, along with the balanced state boundaries, are used to quantify the relative contributions of different strategies and contacts in maintaining or recovering balance in push recovery. The computed boundaries are also incorporated as explicit criteria into a partition-aware push recovery controller that monitors the robot’s COM state to selectively exploit the ankle, hip, or captured stepping strategies. The push recovery simulation experiments demonstrated the validity of the stability boundaries in fully exploiting a humanoid robot’s balancing capability through appropriate balancing actions in response to perturbations. Overall, the system-specific capturability with the whole-body system properties and dynamics outperformed that derived from a typical reduced-order model.