skip to main content


Title: Balancing inverted pendulum cart on inclines using accelerometers
The balance of inverted pendulum on inclined surfaces is the precursor to their control in unstructured environments. Researchers have devised control algorithms with feedback from contact (encoders - placed at the pendulum joint) and non-contact (gyroscopes, tilt) sensors. We present feedback control of Inverted Pendulum Cart (IPC) on variable inclines using non-contact sensors and a modified error function. The system is in the state of equilibrium when it is not accelerating and not falling over (rotational equilibrium). This is achieved when the pendulum is aligned along the gravity vector. The control feedback is obtained from non-contact sensors comprising of a pair of accelerometers placed on the inverted pendulum and one on the cart. The proposed modified error function is composed of the dynamic (non-gravity) acceleration of the pendulum and the velocity of the cart. We prove that the system is in equilibrium when the modified error is zero. We present algorithm to calculate the dynamic acceleration and angle of the pendulum, and incline angle using accelerometer readings. Here, the cart velocity and acceleration are assumed to be proportional to the motor angular velocity and acceleration. Thereafter, we perform simulation using noisy sensors to illustrate the balance of IPC on surfaces with unknown inclination angles using PID feedback controller with saturated motor torque, including valley profile that resembles a downhill, flat and uphill combination. The successful control of the system using the proposed modified error function and accelerometer feedback argues for future design of controllers for unstructured and unknown environments using all-accelerometer feedback.  more » « less
Award ID(s):
1832993
NSF-PAR ID:
10298143
Author(s) / Creator(s):
;
Date Published:
Journal Name:
ASME Letters in Dynamic Systems and Control
ISSN:
2689-6117
Page Range / eLocation ID:
1 to 6
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Over the last few decades, Gyro-Free Inertial Measurement Units (GF-IMUs) have been extensively researched to overcome the limitations of gyroscopes. This research presents a Non-coplanar Accelerometer Array (NAA) for estimating angular velocity with non-specific geometric arrangement of four or more triaxial accelerometers with non-coplanarity constraint. The presented proof of non-coplanar spacial arrangement also provides insights into propagation of the sensor noise and construction of the noise covariance matrices. The system noise depends on the singular values of the relative displacement matrix (between the sensors). A dynamical system model with uncorrelated process and measurement noise is proposed where the accelerometer readings are used simultaneously as process and measurement inputs. The angular velocity is estimated using an Extended Kalman Filter (EKF) that discretizes and linearizes the continuous-discrete time dynamical system. The simulations are performed on a Cube-NAA (Cu-NAA) comprising four accelerometers placed at different vertices of a cube.They analyze the estimation error for static and dynamic movement as the distance between the accelerometers (four accelerometers in cube-orientation) is varied. Here, the system noise is observed to decrease inversely with the length of the cube edge as the arrangement is kept identical. Consequently, the simulation results indicate asymptotic decrease in the standard error of estimation with edge length. The experiments are conducted on a Cu-NAA with five reflective optical markers. The reflective markers are visually tracked using Vicon® to construct the ground truth angular velocity. This unique experimental setup, apart from providing three degrees of rotational freedom of movement, also allows for three degrees of spacial translation (linear acceleration of the Cu-NAA in space). The simulation and experimental results indicate better performance of the proposed EKF as compared to one with correlated process and measurement noises. 
    more » « less
  2. We propose a novel criterion for evaluating user input for human-robot interfaces for known tasks. We use the mode insertion gradient (MIG)—a tool from hybrid control theory—as a filtering criterion that instantaneously assesses the impact of user actions on a dynamic system over a time window into the future. As a result, the filter is permissive to many chosen strategies, minimally engaging, and skill-sensitive—qualities desired when evaluating human actions. Through a human study with 28 healthy volunteers, we show that the criterion exhibits a low, but significant, negative correlation between skill level, as estimated from task-specific measures in unassisted trials, and the rate of controller intervention during assistance. Moreover, a MIG-based filter can be utilized to create a shared control scheme for training or assistance. In the human study, we observe a substantial training effect when using a MIG-based filter to perform cart-pendulum inversion, particularly when comparing improvement via the RMS error measure. Using simulation of a controlled spring-loaded inverted pendulum (SLIP) as a test case, we observe that the MIG criterion could be used for assistance to guarantee either task completion or safety of a joint human-robot system, while maintaining the system’s flexibility with respect to user-chosen strategies. 
    more » « less
  3. Vibrational control is an open loop stabilization technique via the application of highamplitude, high-frequency oscillatory inputs. The averaging theory has been the standard technique for designing vibrational control systems. However, it stipulates too high oscillation frequency that may not be practically feasible. Therefore, although vibrational control is very robust and elegant (stabilization without feedback), it is rarely used in practical applications. The only well-known example is the Kapitza pendulum; an inverted pendulum shose pivot is subject to vertical oscillation. the unstable equilibrium of the inverted pendulum gains asymptotic stability due to the high-frequency oscillation of the pivot. In this paper, we provide a new vibrational control system from Nature; flapping flight dynamics. Flapping flight is a rich dynamical system as a representative model will typically be nonlinear, time-varying, multi-body, multi-time-scale dynamical system. Over the last two decades, using direct averaging, there has been consensus in the flapping flight dynamics community that insects are unstable at the hovering equilibrium due to the lack of pitch stiffness. In this work, we perform higher-order averaging of the time-periodic dynamics of flapping flight to show a vibrational control mechanism due to the oscillation of the driving aerodynamic forces. We also experimentally demonstrate such a phenomenon on a flapping apparatus that has two degrees of freedom: forward translation and pitching motion. It is found that the time-periodic dynamics of the flapping micro-air-vehicle is naturally (without feedback) stabilized beyond a certain threshold. Moreover, if the averaged aerodynamic thrust force is produced by a propeller revolving at a constant speed while maintaining the wings stationary at their mean positions, no stabilization is observed. Hence, it is concluded that the observed stabilization in the flapping system at high frequencies is due to the oscillation of the driving aerodynamic force and, as such, flapping flight indeed enjoys vibrational stabilization. 
    more » « less
  4. This study examines human control of physical interaction with objects that exhibit complex (nonlinear, chaotic, underactuated) dynamics. We hypothesized that humans exploited stability properties of the human-object interaction. Using a simplified 2D model for carrying a “cup of coffee”, we developed a virtual implementation to identify human control strategies. Transporting a cup of coffee was modeled as a cart with a suspended pendulum, where humans moved the cart on a horizontal line via a robotic manipulandum. The specific task was to transport the cart-pendulum system to a target, as fast as possible, while accommodating assistive and resistive perturbations. To assess trajectory stability, we applied contraction analysis. We showed that when the perturbation was assistive, humans absorbed the perturbation by controlling cart trajectories into a contraction region prior to the perturbation. When the perturbation was resistive, subjects passed through a contraction region following the perturbation. Entering a contraction region stabilizes performance and makes the dynamics more predictable. This human control strategy could inspire more robust control strategies for physical interaction in robots. 
    more » « less
  5. This study examines human control of physical interaction with objects that exhibit complex (nonlinear, chaotic, underactuated) dynamics. We hypothesized that humans exploited stability properties of the human-object interaction. Using a simplified 2D model for carrying a “cup of coffee”, we developed a virtual implementation to identify human control strategies. Transporting a cup of coffee was modeled as a cart with a suspended pendulum, where humans moved the cart on a horizontal line via a robotic manipulandum. The specific task was to transport the cart-pendulum system to a target, as fast as possible, while accommodating assistive and resistive perturbations. To assess trajectory stability, we applied contraction analysis. We showed that when the perturbation was assistive, humans absorbed the perturbation by controlling cart trajectories into a contraction region prior to the perturbation. When the perturbation was resistive, subjects passed through a contraction region following the perturbation. Entering a contraction region stabilizes performance and makes the dynamics more predictable. This human control strategy could inspire more robust control strategies for physical interaction in robots. 
    more » « less