Constrained time-efficient and smooth cubic spline trajectory generation for industrial robots

Cao, Binggang; Dodds, G.; Irwin, G.W.

doi:10.1049/ip-cta:19971494

Cited by 36 publications

(26 citation statements)

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“…Table I shows the performance of the quadruped both with and without the cubic spline optimization. We ran 10 trials on each of the terrains, and evaluated the systems using 1) fraction of successful runs, 2) speed over terrain, 3) average number of "recoveries" 5 , and 4) average tracking error (i.e., distance between the planned and actual location) for the moving foot. Perhaps the most obvious benefit of the cubic spline optimization method is that the resulting speeds are faster; this is not particularly surprising, since the splines output by our planner will clearly be more efficient than a simple box pattern over obstacles.…”

Section: Resultsmentioning

confidence: 99%

“…This paper, as well as [5], [6], [7] discuss methods for approximately optimizing the time of the trajectory, but do not consider optimizing the waypoints themselves. The work of Schlemmer et al [9] perhaps bears the most resemblance to our own, as they do consider the modification the cubic spline parameters themselves.…”

Section: Discussion and Related Workmentioning

confidence: 99%

“…Recall that while the position, velocity, etc terms all linearly related by equations (6)- (9), these equations also involve non-linear, non-convex functions of the times. However, there has been previous work in approximately optimizing the times of cubic splines [5], [6], [7], and if the total time of the trajectory is ultimately the most important objective, these techniques can be applied.…”

Section: B Optimization Objectivesmentioning

confidence: 99%

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Task-space trajectories via cubic spline optimization

Kolter

2009

2009 IEEE International Conference on Robotics and Automation

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Abstract-We consider the task of planning smooth trajectories for robot motion. In this paper we make two contributions. First we present a method for cubic spline optimization; this technique lets us simultaneously plan optimal task-space trajectories and fit cubic splines to the trajectories, while obeying many of the same constraints imposed by a typical motion planning algorithm. The method uses convex optimization techniques, and is therefore very fast and suitable for real-time re-planning and control. Second, we apply this approach to the tasks of planning foot and body trajectory for a quadruped robot, the "LittleDog," and show that the proposed approach improves over previous work on this robot. I. INTRODUCTIONIn this paper we consider the task of planning smooth trajectories for robot motion. This is one of the fundamental tasks of robotics, and has received a great deal of attention over the past several decades. One strategy that has proven particularly effective for this task is the use of smooth, parametrized splines to describe trajectories, either in jointspace or task-space. Cubic splines in particular are ubiquitous in robotic applications [1], as they provide a simple means of generating smooth (twice differentiable) trajectories for robot motion.Cubic splines for robot trajectories are typically employed as follows. First, one uses a high-level planning algorithm to generate a series of kinematically feasibly waypoints that the robot should pass through on its way to the goal. Next, one fits the parameters of a cubic spline that passes through all these points; the smoothness of the resulting cubic spline leads to a smoother motion of the robot than would be obtained, for example, by a linear spline that just interpolated between the waypoints. We refer to this as the "two-phase" approach, since the planning and spline fitting are done in separate phases.However, despite their advantages, cubic splines also suffer from a number of drawbacks. The chief problem is that in the typical two-phase application of cubic splines, the high-level waypoint planning is done separate from the cubic spline fitting procedure, which can lead to poor trajectories. To convey this intuition, consider the simple planning task shown in Figure 1 (a): the objective is to move a double pendulum, actuated at both joints, from the start to the goal, while avoiding the obstacle. Figure 1 (b) shows a possible output from a typical planner (for example, a randomized tree planner [2]) and the corresponding cubic spline fit to these waypoints. Due to the stochastic nature of the planner, the waypoints do not lead to a particularly nice final trajectory. Existing trajectory optimization techniques [3] can help mitigate this problem to some degree, but they usually

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Section: Resultsmentioning

confidence: 99%

Section: Discussion and Related Workmentioning

confidence: 99%

Section: B Optimization Objectivesmentioning

confidence: 99%

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Task-space trajectories via cubic spline optimization

Kolter

2009

2009 IEEE International Conference on Robotics and Automation

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“…(Luo et al, 2004) Minimum travelling time path planning was also developed by using polytope method with penalty function. (Cao et al, 1997) Other work involved collision avoidance and minimum-energy path planning (MEPP) or minimum-fuel path planning (MFPP) was undertaken by using method of local variations (MLV). (Seshadri & Ghosh, 1993) In this work, we consider minimization of the energy consumption which is more critical in space applications.…”

Section: Optimal Trajectory Planningmentioning

confidence: 99%

Applications of Optimal Trajectory Planning and Invariant Manifold Based Control for Robotic Systems in Space

Lee¹,

Kojima²,

Trivailo³

2011

Advances in Spacecraft Technologies

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“…See, e.g., (Pfeiffer & Johanni, 1987), for a review of trajectory planning algorithms considering the robot model parameters and torque saturation. Besides, trajectories can also be planned irrespectively of the estimated robot model, i.e., simply by using constraints of position, velocity and acceleration at each time instant, see, e.g., (Cao et al, 1997;Macfarlane & Croft, 2003). Once that the reference trajectory is specified, the task execution is achieved in real time by using a trajectory tracking controller.…”

Section: Introductionmentioning

confidence: 99%

Robot Control Using On-Line Modification of Reference Trajectories

Moreno–Valenzuela¹

2008

Robot Manipulators

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Constrained time-efficient and smooth cubic spline trajectory generation for industrial robots

Cited by 36 publications

References 1 publication

Task-space trajectories via cubic spline optimization

Task-space trajectories via cubic spline optimization

Applications of Optimal Trajectory Planning and Invariant Manifold Based Control for Robotic Systems in Space

Robot Control Using On-Line Modification of Reference Trajectories

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