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

Abstract-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, like 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.

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“…V). This paper is a significantly improved and extended version of the work presented in (Nagarajan 2010;). …”

Section: B Contributionsmentioning

confidence: 98%

Shape space planner for shape-accelerated balancing mobile robots

Nagarajan

Hollis

2013

The International Journal of Robotics Research

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“…In our previous work (Nagarajan 2010;Nagarajan et al 2012b), a trajectory planner that uses only the dynamic constraint equations (Eq. 2) to plan shape trajectories, which when tracked will result in approximate tracking of desired position trajectories was presented.…”

Section: Planning In Shape Spacementioning

confidence: 99%

“…This shape trajectory planner exploits the properties of shape-accelerated balancing systems, and plans motions in shape space that are proportional to desired accelerations in position space. This section presents a brief description of the shape trajectory planner, while a more detailed presentation can be found in (Nagarajan 2010;Nagarajan et al 2012b).…”

Section: Planning In Shape Spacementioning

confidence: 99%

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Integrated motion planning and control for graceful balancing mobile robots

Nagarajan

Kantor

Hollis

2013

The International Journal of Robotics Research

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Abstract-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, pointpoint 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.

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“…In shape-accelerated balancing mobile robots [15] like the ballbot, any non-zero shape change generally results in acceleration in position space. Although we are primarily interested in the motions in position space for navigation purposes, planning for appropriate motions in shape space that result in desired motions in position space is the only way to make balancing mobile robots move with speed and grace.…”

Section: The Ballbotmentioning

confidence: 99%

Integrated planning and control for graceful navigation of shape-accelerated underactuated balancing mobile robots

Nagarajan

Kantor

Hollis

2012

2012 IEEE International Conference on Robotics and Automation

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Abstract-This paper presents controllers called motion policies that achieve fast, graceful motions in small, collisionfree domains of the position space for balancing mobile robots like the ballbot. The motion policies are designed such that their valid compositions will produce overall graceful motions. An automatic instantiation procedure deploys motion policies on a 2D map of the environment to form a library and the validity of their composition is given by a gracefully prepares graph. Dijsktra's algorithm is used to plan in the space of these motion policies to achieve the desired navigation task. A hybrid controller is used to switch between the motion policies. The results of successful experimental testing of two navigation tasks, namely, point-point and surveillance motions on the ballbot platform are presented.

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

Cited by 16 publications

References 14 publications

Shape space planner for shape-accelerated balancing mobile robots

Shape space planner for shape-accelerated balancing mobile robots

Integrated motion planning and control for graceful balancing mobile robots

Integrated planning and control for graceful navigation of shape-accelerated underactuated balancing mobile robots

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