Constant Kinetic Energy Robot Trajectory Planning

In Continuous Path Control (CPC) problems of robot motion planning three tasks have to be solved. These are the path planning, the trajectory planning and the trajectory tracking. The present paper focuses on the problem of trajectory planning. When solving this problem several criteria can be chosen. These can be requirement of minimum time, minimum energy, minimum force, etc. In this article, we deal with constant kinetic energy motion planning. Comparing with time optimal cruising motion, a much smoother trajectory with more power for solving manufacturing tasks is obtained. This is clearly demonstrated by the results of the sample program. The problem of kinematics and dynamics are solved for 2D polar and 2D linear robots

A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories

The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line is comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future

Robot Manipulation Trajectory Planning in Complex Position

The study proposed and demonstrated a strategy smooth trajectory planning to follow the path constrained with time optimal trajectories for the manipulator. The problem in trajectory planning was to find a smooth trajectory function and optimal joint optimisation processes. Such trajectories were obtained by considering the kinematics properties for velocities, accelerations and jerks profiles in joint coordinates for the end-effector to move the path constraints. The method was based on the position profile composed of three polynomial segments such as 4-3-4, 3-5-3 and 3-cubic trajectory and five polynomial segments for 5-cubic trajectory. These polynomial segments combination allowed the analytical solution to the minimum time trajectory problem under consideration of velocity, acceleration and jerk by using Mathematica software. A number of simulations were performed to demonstrate the trajectory methods using robot simulation PUMA 560 model. The robot simulation model was developed using Mechanical Desktop software and the analytical analysis was done using visualNastran software. The simulations showed that the trajectory ability methods for the investigation under varying time ratio conditions and the operations such as Pick and Place Operation (PPO) and Continuous Path (CP). For comparison on varying time ratio 4-3-4 gave a reasonably smooth for normal trajectory condition and a ramp at middle segment to generate a minimum free-space time compared to 3-5-3 and cubic trajectories. For PPO and CP, 4-3-4 trajectory generated a lower values for accelerations and jerks compared to 3-5-3 and cubic trajectories. This showed the 4-3-4 trajectory was the best type of joint interpolated trajectory planning for any path planning operations

Numerical approach of collision avoidance and optimal control on robotic manipulators

Collision-free optimal motion and trajectory planning for robotic manipulators are solved by a method of sequential gradient restoration algorithm. Numerical examples of a two degree-of-freedom (DOF) robotic manipulator are demonstrated to show the excellence of the optimization technique and obstacle avoidance scheme. The obstacle is put on the midway, or even further inward on purpose, of the previous no-obstacle optimal trajectory. For the minimum-time purpose, the trajectory grazes by the obstacle and the minimum-time motion successfully avoids the obstacle. The minimum-time is longer for the obstacle avoidance cases than the one without obstacle. The obstacle avoidance scheme can deal with multiple obstacles in any ellipsoid forms by using artificial potential fields as penalty functions via distance functions. The method is promising in solving collision-free optimal control problems for robotics and can be applied to any DOF robotic manipulators with any performance indices and mobile robots as well. Since this method generates optimum solution based on Pontryagin Extremum Principle, rather than based on assumptions, the results provide a benchmark against which any optimization techniques can be measured

An optimal control strategy for collision avoidance of mobile robots in non-stationary environments

An optimal control formulation of the problem of collision avoidance of mobile robots in environments containing moving obstacles is presented. Collision avoidance is guaranteed if the minimum distance between the robot and the objects is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Furthermore, time consistency with the nominal plan is desirable. A numerical solution of the optimization problem is obtained. Simulation results verify the value of the proposed strategy

The Application of Neural Networks to Optimal Robot Trajectory Planning

Interpolation of minimum jerk robot joint trajectories through an arbitrary number of knots is realized using a hardwired neural network. Minimum jerk joint trajectories are desirable for their similarity to human joint movements and their amenability to accurate tracking. The resultant trajectories are numerical rather than analytic functions of time. This application formulates the interpolation problem as a constrained quadratic minimization problem over a continuous joint angle domain and a discrete time domain. Time is discretized according to the robot controller rate. The neuron outputs define the joint angles (one neuron for each discrete value of time) and the Lagrange multipliers (one neuron for each trajectory constraint). An annealing-type method is used to prevent the network from getting stuck in a local minimum. This paper discusses the optimizing neural network and its application to robot path planning, presents some simulation results, and compares the neural network method with other minimum jerk trajectory planning methods

Practical application of pseudospectral optimization to robot path planning

To obtain minimum time or minimum energy trajectories for robots it is necessary to employ planning methods which adequately consider the platform’s dynamic properties. A variety of sampling, graph-based or local receding-horizon optimisation methods have previously been proposed. These typically use simplified kino-dynamic models to avoid the significant computational burden of solving this problem in a high dimensional state-space. In this paper we investigate solutions from the class of pseudospectral optimisation methods which have grown in favour amongst the optimal control community in recent years. These methods have high computational efficiency and rapid convergence properties. We present a practical application of such an approach to the robot path planning problem to provide a trajectory considering the robot’s dynamic properties. We extend the existing literature by augmenting the path constraints with sensed obstacles rather than predefined analytical functions to enable real world application