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Amit K. Sanyal

Publications and source records attributed to Amit K. Sanyal.

At least 19 recordsLinked to original sources

Iteratively Learning Muscle Memory for Legged Robots to Master Adaptive and High Precision Locomotion

This paper presents a scalable and adaptive control framework for legged robots that integrates Iterative Learning Control (ILC) with a biologically inspired torque library (TL), analogous to muscle memory. The proposed method addresses key challenges in robotic locomotion, including accurate trajectory tracking under unmodeled dynamics and external disturbances. By leveraging the repetitive nature of periodic gaits and extending ILC to nonperiodic tasks, the framework enhances accuracy and generalization across diverse locomotion scenarios. The control architecture is data-enabled, combining a physics-based model derived from hybrid-system trajectory optimization with real-time learning to compensate for model uncertainties and external disturbances. A central contribution is the development of a generalized TL that stores learned control profiles and enables rapid adaptation to changes in speed, terrain, and gravitational conditions-eliminating the need for repeated learning and significantly reducing online computation. The approach is validated on the bipedal robot Cassie and the quadrupedal robot A1 through extensive simulations and hardware experiments. Results demonstrate that the proposed framework reduces joint tracking errors by up to 85% within a few seconds and enables reliable execution of both periodic and nonperiodic gaits, including slope traversal and terrain adaptation. Compared to state-of-the-art whole-body controllers, the learned skills eliminate the need for online computation during execution and achieve control update rates exceeding 30x those of existing methods. These findings highlight the effectiveness of integrating ILC with torque memory as a highly data-efficient and practical solution for legged locomotion in unstructured and dynamic environments.

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Finite-time Stable Pose Estimation on TSE(3) using Point Cloud and Velocity Sensors

This work presents a finite-time stable pose estimator (FTS-PE) for rigid bodies undergoing rotational and translational motion in three dimensions, using measurements from onboard sensors that provide position vectors to inertially-fixed points and body velocities. The FTS-PE is a full-state observer for the pose (position and orientation) and velocities and is obtained through a Lyapunov analysis that shows its stability in finite time and its robustness to bounded measurement noise. Further, this observer is designed directly on the state space, the tangent bundle of the Lie group of rigid body motions, SE(3), without using local coordinates or (dual) quaternion representations. Therefore, it can estimate arbitrary rigid body motions without encountering singularities or the unwinding phenomenon and be readily applied to autonomous vehicles. A version of this observer that does not need translational velocity measurements and uses only point clouds and angular velocity measurements from rate gyros, is also obtained. It is discretized using the framework of geometric mechanics for numerical and experimental implementations. The numerical simulations compare the FTS-PE with a dual-quaternion extended Kalman filter and our previously developed variational pose estimator (VPE). The experimental results are obtained using point cloud images and rate gyro measurements obtained from a Zed 2i stereo depth camera sensor. These results validate the stability and robustness of the FTS-PE.

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Geometric Extended State Observer on SE(3) with Fast Finite-Time Stability: Theory and Validation on a Rotorcraft Aerial Vehicle

This article presents an extended state observer for vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The extended state observer is applicable to a rotorcraft aerial vehicle with a fixed plane of rotors, modeled as an under-actuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, SE(3). The extended state observer is designed to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It guarantees stable convergence of disturbance estimation errors in finite time when the disturbances are constant and finite time convergence to a bounded neighborhood of zero errors for time-varying disturbances. This extended state observer design is based on a Hölder-continuous fast finite time stable differentiator that is similar to the super-twisting algorithm, to obtain fast convergence. Numerical simulations are conducted to validate the proposed extended state observer. The proposed extended state observer is compared with other existing research to show its advantages. A set of experimental results implementing disturbance rejection control using feedback of disturbance estimates from the extended state observer is also presented.

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Geometric Active Disturbance Rejection Control of Rotorcraft on $SE(3)$ with Fast Finite-Time Stability

This article presents a tracking control framework enhanced by an extended state observer for a rotorcraft aerial vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The system is considered as an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, $SE(3)$. The extended state observer is designed to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It guarantees stable convergence of disturbance estimation errors in finite time when the disturbances are constant and finite time convergence to a bounded neighborhood of zero errors for time-varying disturbances. This extended state observer design is based on a Hölder-continuous fast finite time stable differentiator that is similar to the super-twisting algorithm, to obtain fast convergence. A tracking control scheme that uses the estimated disturbances from extended state observer for disturbance rejection, is designed to achieve fast finite-time stable tracking control. Numerical simulations are conducted to validate the proposed extended state observer and tracking control scheme with disturbance rejection. The proposed extended state observer is compared with other existing research to show its supremacy.

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Practice Makes Perfect: an iterative approach to achieve precise tracking for legged robots

Precise trajectory tracking for legged robots can be challenging due to their high degrees of freedom, unmodeled nonlinear dynamics, or random disturbances from the environment. A commonly adopted solution to overcome these challenges is to use optimization-based algorithms and approximate the system with a simplified, reduced-order model. Additionally, deep neural networks are becoming a more promising option for achieving agile and robust legged locomotion. These approaches, however, either require large amounts of onboard calculations or the collection of millions of data points from a single robot. To address these problems and improve tracking performance, this paper proposes a method based on iterative learning control. This method lets a robot learn from its own mistakes by exploiting the repetitive nature of legged locomotion within only a few trials. Then, a torque library is created as a lookup table so that the robot does not need to repeat calculations or learn the same skill over and over again. This process resembles how animals learn their muscle memories in nature. The proposed method is tested on the A1 robot in a simulated environment, and it allows the robot to pronk at different speeds while precisely following the reference trajectories without heavy calculations.

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Asymptotically Stable Optimal Multi-rate Rigid Body Attitude Estimation based on Lagrange-d'Alembert Principle

The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states.

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Input Influence Matrix Design for MIMO Discrete-Time Ultra-Local Model

Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discrete-time, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the Hölder-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the input-dependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controllers.

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Rigid Body Geometric Attitude Estimator using Multi-rate Sensors

A geometric estimator is proposed for the rigid body attitude under multi-rate measurements using discrete-time Lyapunov stability analysis in this work. The angular velocity measurements are assumed to be sampled at a higher rate compared to the attitude. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. In the case when measurements are absent, a discrete-time model for attitude kinematics is assumed in order to propagate the measurements. A discrete-time Lyapunov function is constructed as the sum of a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. A filtering scheme is obtained by discrete-time stability analysis using a suitable Lyapunov function. The analysis shows that the filtering scheme is exponentially stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. Simulation results exhibit convergence of the estimated states to a bounded neighborhood of the actual states.

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Data-Driven Discrete-time Control with Hölder-Continuous Real-time Learning

This work provides a framework for data-driven control of discrete time systems with unknown input-output dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control of the system such that a feasible output trajectory can be tracked. This is made possible by rapid real-time stable learning of the unknown dynamics using Hölder-continuous learning schemes that are designed as discrete-time stable disturbance observers. This observer learns from prior input-output history and it ensures finite-time stable convergence of model estimation errors to a bounded neighborhood of the zero vector if the system is known to be Lipschitz-continuous with respect to outputs, inputs, internal parameters and states, and time. In combination with nonlinearly stable controller designs, this makes the proposed framework nonlinearly stable and robust to disturbances, model uncertainties, and unknown measurement noise. Nonlinear stability and robustness analyses of the observer and controller designs are carried out using discrete Lyapunov analysis. Hölder-continuous Finite-time stable observer and controller designs in this framework help to prove robustness of these schemes and guaranteed convergence of outputs to a bounded neighborhood of the desired output trajectory. A numerical experiment on a nonlinear second-order system demonstrates the performance of this discrete nonlinear model-free control framework.

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Geometric PID-type attitude tracking control on SO(3)

This article develops and proposes a geometric nonlinear proportional-integral-derivative (PID) type tracking control scheme on the Lie group of rigid body rotations, SO(3). Like PD-type attitude tracking control schemes that have been proposed in the past, this PID-type control scheme exhibits almost global asymptotic stability in tracking a desired attitude profile. The stability of this PID-type tracking control scheme is shown using a Lyapunov analysis. A numerical simulation study demonstrates the stability of this tracking control scheme, as well as its robustness to a disturbance torque. In addition, a numerical comparison study shows the effectiveness of the proposed integrator term.

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Nonlinearly Stable Real-Time Learning and Model-Free Control

This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible output trajectory can be tracked by the inputs. Unlike existing model-free or data-driven control approaches, this framework guarantees nonlinear stability. The controller and observer designs in the proposed framework are nonlinearly stable and robust to the unknown dynamics as well as unknown measurement noise. For ease of computer implementation, the framework is developed in discrete time. Nonlinear stability analyses of the discrete-time observers and controllers are carried out using discrete Lyapunov analysis. The unknown input-output dynamics is learnt in real time using a nonlinearly stable observer from prior input-output history. This observer ensures finite-time stable convergence of model estimation errors to zero if the unknown model is constant, and model estimation errors converge to a bounded neighborhood of the zero vector if the model has bounded change in discrete time. Measured outputs are filtered by a finite-time stable observer before use in feedback tracking of a desired output trajectory. Finite-time stable observer design in this framework also ensures that a nonlinear separation principle is in effect for separate controller and observer design. A model-free nonlinearly stable control scheme is then designed to ensure convergence of observed outputs to a desired output trajectory. This control scheme ensures nonlinear finite-time stable convergence of tracking errors to a manifold where the tracking errors decay asymptotically. A numerical experiment on a nonlinear second-order system demonstrates the performance of this nonlinear model-free control framework.

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Geometric structure-preserving optimal control of the rigid body

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition. Instead of discretizing the equations of motion, we use the discrete equations obtained from the discrete Lagrange--d'Alembert principle, a process that better approximates the equations of motion. Within the discrete-time setting, these two approaches are not equivalent in general. The kinematics are discretized using a natural Lie-algebraic formulation that guarantees that the flow remains on the Lie group SO(3) and its algebra so(3). We use Lagrange's method for constrained problems in the calculus of variations to derive the discrete-time necessary conditions. We give a numerical example for a three-dimensional rigid body maneuver.

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Propagation of Uncertainty in Rigid Body Attitude Flows

Motivated by attitude control and attitude estimation problems for a rigid body, computational methods are proposed to propagate uncertainties in the angular velocity and the attitude. The nonlinear attitude flow is determined by Euler-Poincaré equations that describe the rotational dynamics of the rigid body acting under the influence of an attitude dependent potential and by a reconstruction equation that describes the kinematics expressed in terms of an orthogonal matrix representing the rigid body attitude. Uncertainties in the angular velocity and attitude are described in terms of ellipsoidal sets that are propagated through this highly nonlinear attitude flow. Computational methods are proposed, one method based on a local linearization of the attitude flow and two methods based on propagation of a small (unscented) sample selected from the initial uncertainty ellipsoid. Each of these computational methods is constructed using the Lie group variational integrator algorithm, viewed as a discretization of the attitude flow dynamics. Computational results are obtained that indicate (1) the strongly nonlinear attitude flow characteristics and (2) the limitations of each of these methods, and indeed any method, in providing effective global bounds on the nonlinear attitude flow.

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Global Attitude Estimation using Single Direction Measurements

A deterministic attitude estimator for a rigid body under an attitude dependent potential is studied. This estimator requires only a single direction measurement to a known reference point at each measurement instant. The measurement cannot completely determine the attitude, but an attitude estimation scheme based on this measurement is developed; a feasible set compatible with the measurement is described and it is combined with an attitude dynamics model to obtain an attitude estimate. The attitude is globally represented by a rotation matrix, and the uncertainties are described by ellipsoidal sets. A numerical example for a spacecraft in a circular orbit is presented.

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Deterministic Global Attitude Estimation

A deterministic attitude estimation problem for a rigid body in an attitude dependent potential field with bounded measurement errors is studied. An attitude estimation scheme that does not use generalized coordinate representations of the attitude is presented here. Assuming that the initial attitude, angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and its size gives the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The estimation scheme is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized at each measurement instant, and it is global since the attitude is represented by a rotation matrix.

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A Discrete Variational Integrator for Optimal Control Problems on SO(3)

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition. Instead of discretizing the equations of motion, we use the discrete equations obtained from the discrete Lagrange--d'Alembert principle, a process that better approximates the equations of motion. Within the discrete-time setting, these two approaches are not equivalent in general. The kinematics are discretized using a natural Lie-algebraic formulation that guarantees that the flow remains on the Lie group SO(3) and its algebra so(3). We use Lagrange's method for constrained problems in the calculus of variations to derive the discrete-time necessary conditions. We give a numerical example for a three-dimensional rigid body maneuver.

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A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.

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Global Optimal Attitude Estimation using Uncertainty Ellipsoids

A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation error is obtained. Assuming that the initial attitude, the initial angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and the size of the uncertainty ellipsoid measures the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized.

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