Many robotics applications require stabilizing periodic motion rather than equilibrium. The ICPM approach was developed to stabilize periodic motion in underactuated systems. First, Virtual Holonomic Constraints (VHC) were enforced using a continuous controller to ensure the existence of a marginally stable periodic orbit family. Then, intermittent impulsive inputs based on feedback were designed to stabilize the desired periodic orbit that characterizes the desired periodic motion. Recently, the ICPM method has been enhanced to address parameter uncertainty using extended high-gain observers and experimental validation has been performed. Additionally, a method applying multiple impulsive inputs optimally has been developed for faster and more robust orbital stabilization.
Schematic of ICPM approach. Intermittent impulsive inputs are applied on a Poincare section to drive the trajectory towards the desired periodic orbit (red).
N. Kant and R. Mukherjee. Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincare Maps. Systems & Control Letters, 146 (2020): 104813.
Experimental validation of the ICPM approach. Extended high-gain observers are used to mitigate the effect of parameter uncertainty.
N. Kant, R. Mukerjee. Generating Stable Periodic Motion in Underactuated Systems in the Presence of Parameter Uncertainty: Theory and Experiments. Mechatronics, (2024): accepted, under production.
A new approach to designing and stabilizing walking gaits for point-foot planar bipeds was developed. Leveraging VHC, a family of impact-free gaits (no ground-foot impact forces during walking) is obtained, and the desired gait is stabilized using the ICPM approach. This method allows easy adjustment of stride lengths and walking speeds without relying on intensive optimization. It also minimizes impulsive ground impact forces, reducing wear, vibrations, energy loss, and sensor noise.
Stabilization of impact-free gaits of biped using impulsive inputs. The gait parameters such as walking speed and stride lengths can be easily changed.
A. Khandelwal, N. Kant, R. Mukherjee. Design of Impact-Free Gaits for Planar Bipeds and their Stabilization Using Impulsive Control. IEEE Robotics and Automation Letters, (2023).
We shown that impulsive braking inputs causes a negative jump in both the system’s mechanical energy and the Lyapunov-like function characterizing the desired periodic motion based on energy levels. A generalized hybrid control design, combining continuous-time inputs and impulsive braking inputs, was developed to achieve asymptotic stability of periodic motion. Experimental validation was also performed.
We use a hybrid control strategy to demonstrate orbital stabilization of a rotary pendulum. Impulsive braking and continuous inputs are used to achieve swingup.
Kant, N., Mukherjee, R. & Khalil, H. Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking. Nonlinear Dynamics 106, 279–293 (2021)
Workers in the sewing industry often deal with cloth bunching up behind the sewing machine, requiring them to stop, flatten the cloth, and then continue, which reduces productivity and increases stress. A human subject study was conducted to observe how workers remove wrinkles from cloth. The data collected was used to develop a neural network that models these human actions. Efforts are underway to implement this model for robotic wrinkle removal during sewing.
Experimental setup for human subject data collection.
Human action prediction for wrinkle flattening using neural network
The sewing industry experiences high worker dropout due to the demands of precision and speed. Developing a haptic feedback system for the sewing machine foot pedal to provide real-time feedback, allowing sewers to adjust their speed based on sewing quality monitored by a vision system.
Robotic manipulation of objects without grasping is challenging and essential for enhancing the capabilities of practical robots. Solved the juggling problem of a stick, starting in 2-D space and then extending to 3-D space. Juggling was achieved by intermittently applying impact forces to the stick. This task is complex as it involves controlling both position and orientation by hitting the stick at appropriate location. A control design was developed to achieve stable juggling motion.
Nonprehensile manipulation of a stick in 3-D space for stable juggling motion.
Khandelwal, A., Kant, N. & Mukherjee, R. Nonprehensile manipulation of a stick using impulsive forces. Nonlinear Dynamics 111, 113–127 (2023).
Picture yourself strolling along when suddenly you step into a hole. Instinctively, you make rapid adjustments to prevent a fall. Inspired by this scenario, we devised the Impulse Manifold Method, a strategy aimed at restoring stability of underactuated robotic systems. This approach employs brief, powerful bursts of force to swiftly regain stability in robotic systems, ensuring they return to a safe state before potential mishaps occur. We developed a numerical technique (CHART) to estimate and enlarge the region of attraction of an equilibrium configuration. Demonstrated that impulsive inputs can push trajectories from outside to inside this region thereby improving the robustness to external perturbations.
Stabilization of underactuated Pendubot from outside the region of attraction using impulsive inputs.
Kant, N., Mukherjee, R., Chowdhury, D., & Khalil, H. K. (2019). Estimation of the region of attraction of underactuated systems and its enlargement using impulsive inputs. IEEE transactions on robotics, 35(3), 618-632.
Mars missions by NASA have utilized the sky crane touchdown system during the descent phase, where the rover is suspended by tethers to the descent stage. External perturbations can cause the rover to oscillate, potentially compromising the mission. To address this, a nonlinear controller based on the Lyapunov method was designed to rapidly dampen oscillations by adjusting string length. The control design also holds promise for applications in the delivery of objects using drones.
N. Kant. Damping Oscillation of Suspended Payload by Varying String Length. ASME Letters in Dynamic Systems and Control, 2.1 (2022):011003.
Optimal sequence of impulsive inputs were used to raise the potential energy of the reaction wheel pendulum via rest-to-rest maneuvers. The number of inputs can be adjusted based on the actuator input limits.
N. Kant and R. Mukherjee. Impulsive Dynamics and Control of the Inertia-Wheel Pendulum. IEEE Robotics and Automation Letters, 3.4 (2018): 3208-3215.