Motion planning for underactuated bipedal mechanisms with kinematic constraints

This paper deals with the problem of synthesizing smooth piecewise rational spherical motions of an object that satisfies the kinematic constraints imposed by a spherical robot arm with revolute joints. This paper brings together the kinematics of spherical robot arms and recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. The kinematic constraints under consideration are workspace related constraints that limit the orientation of the end link of robot arms. This paper extends our previous work on synthesis of rational motions under the kinematic constraints of planar robot arms. Using quaternion kinematics of spherical arms, it is shown that the problem of synthesizing the Cartesian rational motion of a 2R arm can be reduced to that of circular interpolation in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a spherical 3R arm can be reduced to that of constrained spline interpolation in two separate planes. We present algorithms for the generation of C1 and C2 continuous rational motion of spherical 2R and 3R robot arms.

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Computer Aided Synthesis of Piecewise Rational Motions for Planar 2R and 3R Robot Arms

Journal of Mechanical Design ◽

10.1115/1.2756082 ◽

2006 ◽

Vol 129 (10) ◽

pp. 1031-1036 ◽

Cited By ~ 4

Author(s):

Zhe Jin ◽

Q. J. Ge

Keyword(s):

Motion Planning ◽

Spline Interpolation ◽

Circular Ring ◽

Robot Arm ◽

Kinematic Constraints ◽

Robot Arms ◽

Revolute Joints ◽

Computer Aided ◽

Planar Robot ◽

Circular Interpolation

This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. This paper brings together the kinematics of planar robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Through the use of planar quaternions, it is shown that for the case of a planar 2R arm, the problem of rational motion synthesis can be reduced to that of circular interpolations in two separate planes and that for the case of a planar 3R arm, the problem can be reduced to a combination of circular interpolation in one plane and a constrained spline interpolation in a circular ring on another plane. Due to the limitation of circular interpolation, only C1 continuous rational motions are generated that satisfy the kinematic constraints exactly. For applications that require C2 continuous motions, this paper presents a method for generating C2 continuous motions that approximate the kinematic constraints for planar 2R and 3R robot arms.

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Kinodynamic Motion Planning for an X4-Flyer

Advances in Computational Intelligence and Robotics - Handbook of Research on Advancements in Robotics and Mechatronics ◽

10.4018/978-1-4666-7387-8.ch015 ◽

2015 ◽

pp. 455-474 ◽

Cited By ~ 1

Author(s):

Kimiko Motonaka ◽

Keigo Watanabe ◽

Shoichi Maeyama

Keyword(s):

Motion Planning ◽

Kinematics And Dynamics ◽

Kinematic Constraints ◽

Dynamical Constraints ◽

Flying Robot

This chapter describes kinodynamic motion planning and its application. Kinodynamics is the discipline that tries to solve kinematic constraints and dynamical constraints simultaneously. By using kinodynamic motion planning, control inputs can be generated in a much simpler way, compared to the conventional motion planning that solves kinematics and dynamics separately. After briefly overviewing the kinodynamic motion planning, its application to a flying robot is described in detail.

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Survey of Robot 3D Path Planning Algorithms

Journal of Control Science and Engineering ◽

10.1155/2016/7426913 ◽

2016 ◽

Vol 2016 ◽

pp. 1-22 ◽

Cited By ~ 72

Author(s):

Liang Yang ◽

Juntong Qi ◽

Dalei Song ◽

Jizhong Xiao ◽

Jianda Han ◽

...

Keyword(s):

Path Planning ◽

Motion Planning ◽

Free Path ◽

Optimal Path ◽

Temporal Constraints ◽

Three Dimension ◽

Underwater Robots ◽

Kinematic Constraints ◽

Aerial Robots ◽

Planning Algorithms

Robot 3D (three-dimension) path planning targets for finding an optimal and collision-free path in a 3D workspace while taking into account kinematic constraints (including geometric, physical, and temporal constraints). The purpose of path planning, unlike motion planning which must be taken into consideration of dynamics, is to find a kinematically optimal path with the least time as well as model the environment completely. We discuss the fundamentals of these most successful robot 3D path planning algorithms which have been developed in recent years and concentrate on universally applicable algorithms which can be implemented in aerial robots, ground robots, and underwater robots. This paper classifies all the methods into five categories based on their exploring mechanisms and proposes a category, called multifusion based algorithms. For all these algorithms, they are analyzed from a time efficiency and implementable area perspective. Furthermore a comprehensive applicable analysis for each kind of method is presented after considering their merits and weaknesses.

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Time-optimal smooth-path motion planning for a mobile robot with kinematic constraints

Robotica ◽

10.1017/s0263574797000635 ◽

1997 ◽

Vol 15 (5) ◽

pp. 547-553 ◽

Cited By ~ 22

Author(s):

K. Jiang ◽

L.D. Seneviratne ◽

S.W.E. Earles

Keyword(s):

Mobile Robot ◽

Motion Planning ◽

Visibility Graph ◽

A Algorithm ◽

Kinematic Constraints ◽

Smooth Path ◽

Present Solution ◽

Optimal Motion Planning ◽

Time Optimal ◽

Time Of Travel

This paper presents a novel time-optimal motion planning strategy for a mobile robot with kinematic constraints. The method works in environments in presence of obstacles, without needing to generate the configuration space for the robot. Further, it derives a minimum time first derivative smooth path, as opposed to a minimum distance path which is commonly given by various present solution techniques. The problem is solved in three stages: (i) A reduced visibility graph for a point object is obtained. (ii) The reduced visibility graph is converted into a feasible reduced visibility graph accounting for the size and kinematic constraints of the robot. (iii) The A* algorithm is used to search the feasible reduced visibility graph with the cost function being the time of travel, to obtain a safe, time-optimal, smooth path. The algorithm runs in polynomial time. The method has been tested in computer simulations and test results are presented

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A QP-Based Approach to Kinematic Motion Planning of Multibody Systems

Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2015-48096 ◽

2015 ◽

Cited By ~ 1

Author(s):

Junggon Kim ◽

Rudranarayan Mukherjee

Keyword(s):

Motion Planning ◽

Multibody Systems ◽

Linear Constraints ◽

Software Implementation ◽

Robotic Systems ◽

Time Step ◽

Kinematic Constraints ◽

Cartesian Space ◽

Kinematic Motion ◽

Dual Arm

This article presents a quadratic programming (QP) based approach to local kinematic motion planning of general multibody robotic systems. Given kinematic constraints and targets such as desired positions and orientations in Cartesian space, we find locally optimal joint velocities toward the targets at every time step by formulating the problem into a constrained optimization with a quadratic objective function and linear constraints in terms of the joint velocities. The solution is integrated to obtain the joint displacements at the next time step, and this process is repeated until reaching the targets or converging to a certain configuration. Our formulation based on relative Jacobian is particularly useful in handling constraints on relative motions, which arises in many practical problems such as dual-arm manipulation and self-collision avoidance, in a concise manner. A brief overview of our software implementation and its applications to manipulation and mobility planning of a simulated multi-limbed robot are also presented.

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