Umashankar Nagarajan

State transition, balancing, station keeping, and yaw control for a dynamically stable single spherical wheel mobile robot

Unlike statically stable wheeled mobile robots, dynamically stable mobile robots can have higher centers of gravity, smaller bases of support and can be tall and thin resembling the shape of an adult human. This paper concerns the ballbot mobile robot, which balances dynamically on a single spherical wheel. The ballbot is omni-directional and can also rotate about its vertical axis (yaw motion). It uses a triad of legs to remain statically stable when powered off. This paper presents the evolved design with a four-motor inverse mouse-ball drive, yaw drive, leg drive, control system, and results including dynamic balancing, station keeping, yaw motion while balancing, and automatic transition between statically stable and dynamically stable states.

Trajectory planning and control of an underactuated dynamically stable single spherical wheeled mobile robot

The ballbot is a dynamically stable mobile robot that moves on a single spherical wheel and is capable of omnidirectional movement. The ballbot is an underactuated system with nonholonomic dynamic constraints. The authors propose an offline trajectory planning algorithm that provides a class of parametric trajectories to the unactuated joint in order to reach desired static configurations of the system with regard to the dynamic constraint. The parameters of the trajectories are obtained using optimization techniques. A feedback controller is proposed that ensures accurate trajectory tracking. The trajectory planning algorithm and tracking controller are validated experimentally. The authors also extend the offline trajectory planning algorithm to a generalized case of motion between non-static configurations.

The ballbot: An omnidirectional balancing mobile robot

The ballbot is a human-sized dynamically stable mobile robot that balances on a single ball. Unlike statically stable mobile robots, the ballbot is tall and narrow with a high center of gravity and a small footprint. Moreover, its dynamic stability enables it to be physically interactive. These characteristics make it better suited to navigate and interact in cluttered human environments. This paper presents the evolved hardware design of the ballbot with a four-wheel inverse mouse-ball drive to actuate the ball, and a yaw drive mechanism that enables unlimited rotation about its vertical axis. The ballbot also has a triad of legs that provide static stability when powered down. This paper presents a detailed description of the ballbot’s control architecture, and it presents several experimental results that demonstrate its balancing and locomotion capabilities. This paper also presents a trajectory planning algorithm that plans for body lean motions, which, when tracked, result in the desired rest-to-rest motions of the robot. Finally, the paper illustrates some interesting human–robot physical interaction behaviors that can be achieved as a result of the ballbot’s dynamic stability.

Dynamic Constraint-based Optimal Shape Trajectory Planner for Shape-Accelerated Underactuated Balancing Systems

This paper presents an optimal shape trajectory planner for shape-accelerated underactuated balancing systems, which are destabilized by gravitational forces. These systems have unactuated shape variables and fully actuated external variables. They also have the same number of actuated and unactuated degrees of freedom. Their equations of motion result in nonholonomic acceleration/dynamic constraints, which relate the acceleration of external variables to the position, velocity and acceleration of shape variables. This paper describes a procedure to use the dynamic constraints for planning shape trajectories, which when tracked will result in optimal tracking of desired external configuration trajectories. Examples of planned optima l shape trajectories for the 3D ballbot system, which is a 3D omnidirectional wheeled inverted pendulum, are also presented.

Human-robot physical interaction with dynamically stable mobile robots

Developed by Prof. Ralph Hollis in the Microdynamic Systems Laboratory at Carnegie Mellon University, Ballbot is a dynamically stable mobile robot moving on a single spherical wheel providing omni-directional motion. Unlike statically stable mobile robots, dynamically stable mobile robots can be tall and skinny with high center of gravity and small base. The ball drive mechanism is a four motor inverse mouse-ball setup. An Inertial Measuring Unit (IMU) and encoders on the motors provide all information needed for full-state feedback. Ballbot has three legs that provide static stability when powered down and is capable of auto-transitioning from the statically stable state to the dynamically stable state and vice versa. It is also capable of yaw rotation about its vertical axis. An absolute encoder provides the relative angle between the IMU and the ball drive unit. We wish to demonstrate Human-Robot Physical Interaction with dynamically stable mobile robots using Ballbot as an example. The balancing controller on Ballbot is extremely robust to disturbances like shoves, kicks and collisions with furniture and wall. Due to its dynamic stability, Ballbot can be moved around with very little effort. Physically directing a heavy statically stable mobile robot can be a difficult task, whereas Ballbot can be moved around with just a single finger. Similarly, while moving, Ballbot can be stopped with very little effort. We have developed some basic behaviors that enable Ballbot to detect human intentions with the physical interaction it has using just the encoder and IMU data. For example, given a soft push, Ballbot tries to stick to its position on the floor, whereas, when given a hard push, it moves away from its current location and station-keeps at a different point on the floor. We also present our initial results in developing a Learn-Repeat behavior in Ballbot, where in during the Learn mode, the user drives Ballbot around and it remembers the path travelled, and during the Repeat mode, Ballbot attempts to repeat the path learnt. We are in the process of adding stereo cameras and laser range finders to the robot, which will help us explore and extend more areas of Human-Robot Interaction.

Generalized direction changing fall control of humanoid robots among multiple objects

Humanoid robots are expected to share human environments in the future and it is important to ensure safety of their operation. A serious threat to safety is the fall of a humanoid robot, which can seriously damage both the robot and objects in its surrounding. This paper proposes a strategy for planning and control of fall. The controllers objective is to prevent the robot from hitting surrounding objects during a fall by modifying its default fall direction. We have earlier presented such a direction-changing fall controller in [1]. However, the controller was applicable only when the robots surrounding contained a single object. In this paper we introduce a generalized approach to humanoid fall-direction control among multiple objects. This new framework algorithmically establishes a desired fall direction through assigned scores, considers a number of control options, and selects and executes the best strategy. The fall planner is also able to select “No Action” as the best strategy, if appropriate. The controller is interactive and is applicable for fall occurring during upright standing or walking. The fall performance is continuously tracked and can be improved in real-time. The planning and control algorithms are demonstrated in simulation on an ASIMO-like humanoid robot.

Planning in high-dimensional shape space for a single-wheeled balancing mobile robot with arms

The ballbot with arms is an underactuated balancing mobile robot that moves on a single ball. Achieving desired motions in position space is a challenging task for such systems due to their unstable zero dynamics. This paper presents a novel approach that uses the dynamic constraint equations to plan shape trajectories, which when tracked will result in optimal tracking of desired position trajectories. The ballbot with arms has shape space of higher dimension than its position space and therefore, the procedure uses a user-defined weight matrix to choose between the infinite number of possible combinations of shape trajectories to achieve a particular desired trajectory in position space. Experimental results are shown on the real robot where different motions in position space are achieved by tracking motions of either the body lean angles, or the arm angles or combinations of both.

Hybrid control for navigation of shape-accelerated underactuated balancing systems

This paper presents a hybrid control strategy for navigation of shape-accelerated underactuated balancing systems with dynamic constraints. It extends the concept of sequential composition to perform discrete state-based switching between asymptotically convergent control policies to produce a globally asymptotically convergent feedback policy. The individual control policies consists of an external trajectory planner, a shape trajectory planner, an external trajectory tracking controller and a balancing controller. The paper also presents an integrated planning and control procedure, wherein standard graph-search algorithms are used to plan for the sequence of control policies that will help the system achieve a navigation goal. Simulation results of the 3D ballbot system navigating an environment with static obstacles to reach the goal position are also presented.

Integrated motion planning and control for graceful balancing mobile robots

This paper presents an integrated motion planning and control framework that enables balancing mobile robots to gracefully navigate human environments. A palette of controllers called motion policies is designed such that balancing mobile robots can achieve fast, graceful motions in small, collision-free domains of the position space. The domains determine the validity of a motion policy at any point in the robot’s position state space. An automatic instantiation procedure that generates a motion policy library by deploying motion policies from a palette on a map of the environment is presented. A gracefully prepares relationship that guarantees valid compositions of motion policies to produce overall graceful motion is introduced. A directed graph called the gracefully prepares graph is used to represent all valid compositions of motion policies in the motion policy library. The navigation tasks are achieved by planning in the space of these gracefully composable motion policies. In this work, Dijsktra’s algorithm is used to generate a single-goal optimal motion policy tree, and its variant is used to rapidly replan the optimal motion policy tree in the presence of dynamic obstacles. A hybrid controller is used as a supervisory controller to ensure successful execution of motion policies and also successful switching between them. The integrated motion planning and control framework presented in this paper was experimentally tested on the ballbot, a human-sized dynamically stable mobile robot that balances on a single ball. The results of successful experimental testing of two navigation tasks, namely, point-point and surveillance motions are presented. Additional experimental results that validate the framework’s capability to handle disturbances and rapidly replan in the presence of dynamic obstacles are also presented.

Shape space planner for shape-accelerated balancing mobile robots

This paper introduces shape-accelerated balancing systems as a special class of underactuated systems wherein their shape configurations can be mapped to the accelerations in the position space. These systems are destabilized by gravitational forces and have non-integrable constraints on their dynamics. Balancing mobile robots, such as the ballbot, are examples of such systems. The ballbot is a human-sized dynamically stable mobile robot that balances on a single ball. This paper presents a shape trajectory planner that uses dynamic constraint equations to plan trajectories in the shape space, which when tracked will result in approximate tracking of desired position trajectories. The planner can handle systems with more shape variables than position variables, and can also handle cases where a subset of the shape variables is artificially constrained. Experimental results are shown on the ballbot with arms where different desired position space motions are achieved by tracking shape space motions of either body lean angles, or arm angles or combinations of the two; and also by tracking only the body lean motions while the arm angles are artificially constrained.