Joint Trajectory Generation Research Articles

A real-time joint trajectory planner for dynamic walking bipeds in the sagittal plane

A real-time joint trajectory generator for planar walking bipeds is proposed. This trajectory planner generates dynamically stable motion patterns by using a set of objective locomotion parameters as its input, and by tuning and exploiting the natural upper body dynamics. The latter can be determined and manipulated by using the angular momentum equation. Basically, trajectories for hip and swing foot motion are generated, which guarantee that the objective locomotion parameters attain certain prescribed values. Additionally, the hip trajectories are slightly modified such that the upper body motion is steered naturally, meaning that it requires practically no actuation. This has the advantage that the upper body actuation hardly influences the position of the Zero Moment Point. The effectiveness of the developed strategy is demonstrated by simulation results.

Control architecture for the pneumatically actuated dynamic walking biped “Lucy”

This paper reports on the control structure of the biped Lucy. The robot is actuated with pleated pneumatic artificial muscles which have interesting characteristics that can be exploited for legged machines. They have a high power to weight ratio, an adaptable compliance and they reduce impact effects. The considered control structure can be divided into two parts: a real-time joint trajectory generator and a trajectory tracking controller. The latter consists of a computed torque controller, a delta- p unit, a PI controller and a bang–bang pressure controller. The trajectory generator provides polynomial joint trajectories while the computed torque in combination with the delta- p unit calculates the required muscle pressure levels. The PI and bang-bang controller work at pressure level to cope with modelling errors and to set the pressures in each muscle. The proposed control architecture is evaluated with a full hybrid dynamic simulation model of the biped. This simulator combines the dynamical behaviour of the robot with the thermodynamical effects that take place in the muscle-valves system. The observed hardware limitations of the real robot and expected model errors are taken into account in order to give a realistic qualitative evaluation of the control performance and to test its robustness. At this stage a controller is designed for and evaluated during the single support phase only. In the double support phase the robot is over-actuated and consequently other control strategies are necessary. Additionally, preliminary results of a walking motion of the real robot with both feet in the air are given. These show promising results concerning tracking performance of the proposed control architecture. The experimental results confirm that the pneumatic tracking system can be used for a dynamic application such as a biped walking robot.

Programming full-body movements for humanoid robots by observation

The formulation and optimization of joint trajectories for humanoid robots is quite different from this same task for standard robots because of the complexity of humanoid robots’ kinematics and dynamics. In this paper we exploit the similarity between human motion and humanoid robot motion to generate joint trajectories for humanoids. In particular, we show how to transform human motion information captured by an optical tracking device into a high dimensional trajectory for a humanoid robot. We propose an automatic approach to relate humanoid robot kinematic parameters to the kinematic parameters of a human performer. Based on this relationship we infer the desired trajectories in robot joint space. B-spline wavelets are utilized to efficiently represent the trajectories. The density of the basis functions on the time axis is selected automatically. Large-scale optimization techniques are employed to solve the underlying computational problems efficiently. We applied our method to the task of teaching a humanoid robot how to make various naturally looking movements.

A joint trajectory generator for motion recovery

This paper describes an adaptive S-curve used to recover a tool path upon a system crash in the Windows operating system (OS). For a mechanism such as a robot or machine tool, the joint values, being delivered as setpoints to the servo-controller, are dynamically recorded by the real-time operating system also residing on the computer. The real-time OS can control the abort and record pertinent motion data after Windows OS crash.Upon system recovery, the recovery trajectory generator examines the setpoints intervals to determine the current slow joint. At every trajectory step, and for the current slow joint, the S-curve velocity profile applies the joint entry state (position, speed, acceleration, and jerk) to interpolate the motion between the setpoints in a reverse direction. The other joints are proportionally interpolated (slowed) so that they pass through each setpoint simultaneously with the slow joint, but in a reverse direction.The trajectory algorithm is optimal since the slow joint always uses the maximum allowable jerk to change the profile speed and acceleration for each trajectory step.

Computational Intelligence Based Approach for the Joint Trajectory Generation of Cooperative Robotic Systems

We discuss here the implementation aspects of recently developed tools of computational intelligence as applied to joint trajectory generation of a class of multi-joint cooperative robotic systems. This is an issue closely related to the inverse kinematics problem which usually represents a heavy computational burden on the processing power of any complex robotic structure. High nonlinearities, heavy coupling between the degrees of freedom, and time variant configuration of the robot structure heavily contribute to these difficulties. Soft computing techniques have surged in recent years as effective computational tools for emulating the human capabilities when dealing with complex systems. Some of them are used here to synthesize approaches capable of substantially improving the solving of the inverse kinematics problem for a class of robotic systems and help in generating the joint trajectories in a faster way. Comparative results are provided in terms of accuracy and CPU time required for the execution of different trajectories.

Minimum time on-line joint trajectory generator based on low order spline method for industrial manipulators

In this paper, we propose the use of a low order polynomial method named 3-Cubic method to generate minimum time on-line joint trajectory for an industrial manipulator. A 3-Cubic Spline between two end points consists of a set of three cubic splines, which not only give an analytical solution to minimize travel time with velocity, acceleration and jerk constraints but also provides the continuity till second derivative of position (i.e. acceleration). This results in a position trajectory being dynamically balanced. This leads to the generation of a new type of trajectory named 3-Cubic Linear Segment with Trapezoidal Transition (3CLSTT) trajectory. In this trajectory generation, duration of constant acceleration/deceleration and constant velocity phases are calculated according to the requirements of maximum limiting values of velocity and acceleration thus traversing the trajectory in minimum possible time. Wandering (undershoot/overshoot) is completely eliminated in the resulting trajectories with limited computational effort.

Motion control of non-fixed base robotic manipulators

Robotic manipulators mounted on spacecraft experience a number of kinematic, dynamic, and control problems because the motion of the spacecraft is affected by the robot motion. In this paper, the general three dimensional equations of motion are derived for an n link manipulator mounted on a non-fixed base object. Instead of performing a single inverse kinematic calculation at the beginning of a movement to determine the required joint setpoints, multiple inverse kinematic updates are done throughout a movement. The updating sequence is determined by an optimal inverse kinematic updating algorithm. This motion control algorithm is based on experimental simulation results performed in Matlab and a set of performance indices that are used as guidelines. Simple PD joint controllers and a special joint trajectory generator are used for servoing the manipulator joints for a planar robot application. The derived motion control techniques incorporate the base motion without base motion control.

Cooperative Motion Planning for Grasp-Work Type Mainpulator System.

A motion planning problem of cooperative multiple manipulator system carrying on the grinding work or similar works to the object is considered. One manipulator holds the object rigidly and the other holds the tool and works on the object's surface. At the contact point between the object and the tool there exists friction, so that interaction forces must be taken into considerations in dynamics of manipulators and the object. We only specify the tool task on the object's surface, so the object and manipulators can move arbitrary paths in the world coordinates frame. Using these degrees of freedom, we propose an algorithm to generate joint trajectories for cooperative grasp-work type manipulator system to accomplish the specified task effectively.

An approach to time-optimal, smooth and collision-free path planning in a two robot arm environment

SummaryAn approach to time-optimal smooth and collision-free path planning for two industrial robot arms is presented, where path planning and joint trajectory generation are integrated. A suitable objective function, combining the requirements of time optimality and path smoothness, is proposed, which is subject to the continuity of joint trajectories, limits on their rates of change and collision-free constraints. Fast and effective collision detection for the arms is achieved using the Kuhn- Tucker conditions along with the convexity of the distance function and relying on geometrical relationships between cylinders. Nonlinear optimization is used to solve this path planning problem. The feasibility of this method is illustrated both by simulation and by experimental results.

Redundant arm kinematic control with recurrent loop

A new method for generating redundant arm inverse kinematic solutions based on the iterative update of joint vectors is presented. A novel neural network architecture with a recurrent loop is then formed based on the proposed method. In the proposed method, the pseudoinverse of the gradient of a Lyapunov function is defined in the joint space to update the joint vector toward a solution. This differs from the conventional methods based on the Jacobian pseudoinverse or Jacobian transpose. This paper establishes explicit convergence control schemes to achieve fast and stable convergence: 1) the convergence speed is enhanced by modifying the convergence dynamics based on terminal attractors, and 2) the convergence stability is ensured by the adaptive selection of update intervals based on the stability condition derived in this paper. The proposed neural network consists of a feedforward network and a feedback network forming a recurrent loop. The feedforward network is a multilayer network with hidden units having sinusoidal activation functions. As such, it computes accurately the forward kinematic solutions with simple training. The feedback network is derived from the feedforward network and computes joint vector updates. The proposed neural network has definite advantages over conventional neural networks for robot arm kinematic control, because it can not only handle redundant arm kinematic control, but can also provide an accurate computation of forward and inverse kinematic solutions with very simple training. The simulation results demonstrate that the proposed method is effective for the real-time kinematic control of a redundant arm as well as the real-time generation of collision-free joint trajectories.

Joint trajectory generation for redundant robots in an environment with obstacles

AbstractCollision avoidance is an absolutely essential requirement for a robot to complete a task in an environment with obstacles. For kinematically redundant robots, collision avoidance can be achieved by making full use of the redundancy. In this article, the problem of determining collision‐free joint space trajectories for redundant robots in an environment with multiple obstacles is considered, and the “command generator” approach is employed to generate such trajectories. In this approach, a nondifferentiable distance objective function is defined and is guaranteed to increase wherever possible along the trajectory through a vector in N(J), the null space of Jacobian matrix J. Algorithms that implement this nondifferentiable optimization problem are fully developed. It is shown that the proposed collision‐free trajectory generation scheme is efficient and practical. Extensive simulation results of a four‐link robot example are presented and analyzed.

Trajectory Planning and Control System for a SCARA Robot.

The SCARA robot control system, which comprises environment monitoring, collision-free path planning, joint trajectory generation and trajectory control, is developed. In environment monitoring, the work space is displayed on a CRT through a TV camera and obstacles are then interactively modeled. The collision-free path is planned based on the configuration space method, and the shortest path is heuristically obtained. The path is described by a set of joint trajectories using the B-spline curve. The trajectories are iteratively improved to optimize the specified performance index considering the robot dynamics. The generated trajectories are used as reference joint trajectories to control the robot. Control parameters are also determined according to the identification of the robot. This system is confirmed to be effective throughout experiments.

An adaptive scheme for robot joint trajectory generation

AbstractIt has been shown recently that robot inverse kinematic transformation can be easily carried out by using a nonlinear dynamic system called “joint space command generator.” In this paper, an adaptive version of the command generator is proposed. The main feature of this command generator is that the inverse Jacobian is estimated on‐line (using least‐squares algorithms), thus the explicit form of the inverse Jacobian is not required. Since the Jacobian is dependent on the end‐effector orientation representation, the adaptive command generator is then inherently flexible in accommodating any choice of orientation representation during Cartesian trajectory planning. The only knowledge required is the forward kinematics of the robot. Thus inverse kinematic transformation of robot trajectories can be carried out with a minimum amount of kinematic information. Extensive simulation studies of the proposed scheme have been carried out which showed that the adaptive command generator is computationally feasible and highly accurate. Different orientation representations have been tested with equal success. Some typical simulation results are presented to illustrate the performance of the adaptive command generator.

A three-dimensional model for leg and foot kinematical studies

Legged robots based on one degree-of-freedom reconfigurable planar leg mechanisms, that are capable of generating multiple useful gaits, are highly desired due to the possibility of handling environments and tasks of high complexity while maintaining simple control schemes. An essential consideration in these reconfigurable legged robots is to attain stability in motion, at rest as well as while transforming from one configuration to another with the minimum number of legs as long as the full range of their walking patterns, resulting from the different gait cycles of their legs, is achieved. To this end, in this paper, we present a method for the generation of input joint trajectories to properly synchronize the movement of quadruped robots with reconfigurable legs. The approach is exemplified in a four-legged robot with reconfigurable Jansen legs capable of generating up to six useful different gait cycles. The proposed technique is validated through simulated results that show the platform׳s stability across its six feasible walking patterns and during gait transition phases, thus considerably extending the capabilities of the non-reconfigurable design.

Joint trajectories of mechanical manipulators for Cartesian path approximation

Methods of joint trajectory generation for mechanical manipulators using X-spline and quartic spline functions are presented. A sequence of Cartesian knots, i.e. positions and orientations of the hand, are selected from the desired Cartesian path. Joint values corresponding to these selected knots are solved from the kinematic equation. Approximate joint paths are constructed by interpolating these joint positions. At any instant, two or more future knots need to be known in advance in order to determine the current joint trajectories. Approximate errors for Cartesian paths are discussed. An illustrative example is used for comparing these trajectories to other existent polynomial-type trajectories.