Motion Planning of a Nonholonomic Multibody System Using Genetic Algorithm

In the case that the total angular momentum conservation about the system center of mass, a torque-free spacecraft system with space manipulators becomes the nonholonomic control system. Due to the nonholonomic characteristic, the motion planning and control of a nonholonomic system is much more difficult than that of a conventional. In terms of the nonholonomic characteristic, the three-dimensional attitude control problem of the free floating space manipulators is investigated. The mathematical model of attitude control of rigid spacecraft with space manipulators is obtained. The control problem of the spacecraft attitude becomes a motion planning problem for a drift free control system. The control input rule is expressed by Fourier orthonormal basis and coefficient vector. Based on the optimal motion planning, the particle swarm optimization algorithm is proposed for free floating space manipulators. The results of numerical simulation indicate that this approach is effective for the motion planning problem of space manipulators.

The chained form system is a controllable nonholonomic system, wherein the motion planning and control had been often researched. Therefore, based on the chained form transformation, the motion planning and control of nonholonomic system can be researched by the motion planning and control of chained form system. According to this thought, motion planning and control of nonholonomic multi-joint manipulator were researched in this paper. A method of nonholonomic motion planning and control was proposed by the chained form transformation, and validity of the method was proved by computer simulation

The optimal attitude control problem of a rigid spacecraft with flywheels that provide two control input is treated. In the case that the total angular momentum of the system is zero, the nonholonomic behavior of underactuated system is employed to develop the dynamical equations of the system. The problem of reorienting a rigid spacecraft is formulated as an optimal control problem for a drift free control system. The genetic algorithm is proposed to achieve angular rate input law of two flywheels and the optimal reorientation of a spacecraft. By use of the wavelet method, the control input law is approximated by the discrete orthogonal wavelets. The numerical simulation indicates that genetic algorithm and wavelet approximation are effective approaches to solve the optimal reorientation problem.

Dynamics modeling and motion planning for snakeboard systems were investigated, and a hybrid optimization strategy based on the genetic algorithm (GA) and the Gauss pseudospectral method (GPM) was presented. Firstly, the Euler-Lagrange equations for the snakeboard system were derived based on the Riemannian manifold and the affine connection theory in differential geometry. The configuration space of the snakeboard corresponds to the manifold space, the velocity space corresponds to the tangent space, the torque space corresponds to the cotangent space, and the inertia matrix provides a Riemannian measure on the manifold. The set of admissible velocities were represented by the appropriate bases to simplify the kinematics equations. Then the optimal motion planning problem was transformed into a nonlinear programming problem with the GPM. The optimal trajectory and the optimal control inputs were obtained with the sequential quadratic programming (SQP) algorithm. The GA was applied to generate the initial values of the GPM. Finally, through numerical simulation, the optimal trajectory agrees well with actual conditions, and the control inputs match the various constraints closely. The results demonstrate the effectiveness of the proposed method.

Motion planning for complex dynamic systems such as helicopters is a challenging problem due to non-holonomic and nonlinear differential constraints. Approaches for optimal kinodynamics motion planning have only been demonstrated for simple dynamic systems such as Dubins car or linear systems. In this paper we present Closed-loop FMT* (CL-FMT*) which is an extension of FMT* [7] that uses closed-loop prediction. With closed-loop prediction the computationally intense two-point-boundary-value steering procedure can be avoided. We describe the effectiveness of CL-FMT* compared to CL-RRT*. We then demonstrate the use of CL-FMT* for helicopter landing trajectory planning with realistic dynamics constrains.

Robots operating in the real world must combine task planning for reasoning about what to do with motion planning for reasoning about how to do it -- this is known as task and motion planning. One promising approach for task and motion planning is Logic Geometric Programming (LGP) which integrates a logical layer and a geometric layer in an optimization formulation. The logical layer describes feasible high-level actions at an abstract symbolic level, while the geometric layer uses continuous optimization methods to reason about motion trajectories with geometric constraints. In this paper we propose a new approach for solving task and motion planning problems in the LGP formulation, that leverages state-of-the-art diverse planning at the logical layer to explore the space of feasible logical plans, and minimizes the number of optimization problems to be solved on the continuous geometric layer. To this end, geometric infeasibility is fed back into planning by identifying prefix conflicts and incorporating this back into the planner through a novel multi-prefix forbidding compilation. We further leverage diverse planning with a new novelty criteria for selecting candidate plans based on the prefix novelty, and a metareasoning approach which attempts to extract only useful conflicts by leveraging the information that is gathered in the course of solving the given problem.

Abstract. This paper addresses the motion planning problem in non-holonomic robotic systems. The system's kinematics and dynamics are represented as a control affine system with outputs. The problem is defined in terms of the end-point map of this system, using the endogenous configuration space approach. Special attention is paid to the multiple-task motion planning problem, i.e. a problem that beyond the proper motion planning task includes a number of additional tasks. For multiple-task motion planning two strategies have been proposed, called the egalitarian approach and the prioritarian approach. Also, two computational strategies have been launched of solving the motion planning problem: the parametric and the non-parametric. The motion planning and computational strategies have been applied to a motion planning problem of the trident snake robot. Performance of the motion planning algorithms is illustrated with computer simulations.

Learning from Demonstration (LfD) is a family of methods used to teach robots specific tasks. It is used to assist them with the increasing difficulty of performing manipulation tasks in a scalable manner. The state-of-the-art in collaborative robots allows for simple LfD approaches that can handle limited parameter changes of a task. These methods however typically approach the problem from a control perspective and therefore are tied to specific robot platforms. In contrast, this paper proposes a novel motion planning approach that combines the benefits of LfD approaches with generic motion planning that can provide robustness to the planning process as well as scaling task learning both in number of tasks and number of robot platforms. Specifically, it introduces Dynamical Movement Primitives (DMPs) based LfD as initial trajectories for the Stochastic Optimization for Motion Planning (STOMP) framework. This allows for successful task execution even when the task parameters and the environment change. Moreover, the proposed approach allows for skill transfer between robots. In this case a task is demonstrated to one robot via kinesthetic teaching and can be successfully executed by a different robot. The proposed approach, coined Guided Stochastic Optimization for Motion Planning (GSTOMP) is evaluated extensively using two different manipulator systems in simulation and in real conditions. Results show that GSTOMP improves task success compared to simple LfD approaches employed by the state-of-the-art collaborative robots. Moreover, it is shown that transferring skills is feasible and with good performance. Finally, the proposed approach is compared against a plethora of state-of-the-art motion planners. The results show that the motion planning performance is comparable or better than the state-of-the-art.

Robots used for inspection, package deliveries, moving of goods, and other logistics operations are often required to visit certain locations within specified time bounds. This gives rise to a challenging problem as it requires not only planning collision-free and dynamically feasible motions but also reasoning temporally about when and where the robot should be. While significant progress has been made in integrating task and motion planning, there are still no effective approaches for multigoal motion planning when both dynamics and time windows must be satisfied. To effectively solve this challenging problem, this paper develops an approach that couples temporal planning over a discrete abstraction with sampling-based motion planning over the continuous state space of feasible motions. The discrete abstraction is obtained by imposing a roadmap that captures the connectivity of the free space. At each iteration of a core loop, the approach first invokes the temporal planner to find a solution over the roadmap abstraction. In a second step, the approach uses sampling to expand a motion tree along the regions associated with the discrete solution. Experiments are conducted with second-order ground and aerial vehicle models operating in complex environments. Results demonstrate the efficiency and scalability of the approach as we increase the number of goals and the difficulty of satisfying the time bounds.

A problem of motion planning and coordination of compact formations of ground and aerial robots will be tackled in this paper. The scenarios when the formation composed from Unmanned Ground Vehicles (UGVs) and Unmanned Aerial Vehicles (UAVs), in particular Micro Aerial Vehicles (MAVs), has to reverse the direction of movement to fulfil task of collisionfree motion to a target zone will be solved. The presented motion planning and stabilization approach provides an effective technique to enable deployment of closely cooperating teams of robots in outdoor as well as indoor environment. The formation to target region problem is solved using a Model Predictive Control (MPC) methodology and the formation driving concept is based on a virtual-leader-follower approach. The mentioned MPC based process is used for trajectory planning and control of a virtual leader and also for control and stabilization of followers (MAVs and UGVs). The proposed approach is verified with numerous simulations and hardware experiments.

This paper addresses a problem of optimal motion planning of mobile platforms amidst obstacles, considering the mobile platform dynamics. Due to nonholonomic constraints, actuator constraints, and state constraints by obstacle avoidance, the planning problem of mobile platform with two independently driven wheels is a complicated one. In this study, a dynamical model for the mobile platform is presented, including nonholonomic kinematic constraints. The idea of a path parameter is introduced to simplify the planning problem by considering the dynamics and nonholonomic constraints. Using the path parameter, the optimal motion planning problem is divided into two sub-problems: 1) time-optimization of trajectory along specified path, and 2) search for optimal path. Then two methods are proposed the solve the problems using the path parameter and parametrization by B-spline function. Finally, quasi-time-optimal solution for the original problem are planned by combining the two methods. Numerical examples show effectiveness of the motion planner.

Optimal control of nonholonomic motion planning for a free-falling cat

Recently, it is expected to develop an autonomous robot working in a living environment. Motion planning is very important for an autonomous mobile robot, but kinematic constraints and dynamic constraints are generally solved separately in conventional motion planning. In this research, a simpler way of deciding the control input for an autonomous mobile robot, which is described by a highly nonlinear model in a multi-dimensional space, is proposed by solving kinematic constraints and dynamic constraints simultaneously, under the kinodynamic motion planning based on a harmonic potential field (HPF). In this paper, a quadrotor that is very attractive as an aerial robot due to its high maneuverability, is assumed to be a controlled object, and it is aimed at guiding the quadrotor to an arbitrary target point while avoiding obstacles. Then, three types of controllers for kinodynamic motion planning based on an HPF, which were developed for point mass control, are extended to be applied to the quadrotor. The extended controllers are compared each other in trajectory, amplitude of attitude, and arrival time through some flight simulations. Moreover, multiple gains included in the proposed controllers are optimized automatically by using genetic algorithm (GA), in order to realize highly accurate control. Flight simulation in an untrained environment, which is different from the environment that the gains were selected by GA, is also conducted, and it is confirmed that the quadrotor can move onto the target point with the same gains while avoiding obstacles.

Omni-directional Wheeled Mobile Robots (Omni-WMR) are holonomic system able to move sideways. They have locomotive advantage and are widely deployed in a larger range of application fields, especially in narrowly constrained service-styled manufacturing industries. To ensure smooth motion and full development of locomotive advantages, motion planning draws great attention. Thanks to the mechanism of powered caster wheel (PCW), the motion of Omni-WMR can be decoupled. The collective motion can be decomposed into dimensions of x, y and θ, then planned independently and superposed. In this way trajectory can be planned in the Cartesian space, and later on transformed to the joint space through inverse instantaneous kinematics model for actuation of the motor at each joint. Quintic-polynomial interpolation is used for the case of start to goal with only initial and final configurations known, and piecewise-cubic-spline interpolation is applied for the case of a sequence of intermediate way-points known in the configuration space as input. Here the geometric points for the robot to go through are assumed to be known as a priori without loss of generality. The approaches are implemented in python on ROS (Robot Operating System), and these modular ROS packages are tested on a physical Omni-WMR developed at our lab. Meanwhile, these ROS packages are also tested equivalently in a virtual simulation environment modelled using ROS stage simulator. The experimental results have proved that the motion planning algorithms are able to generate smooth velocity profile for the robot to achieve the goal, which have validated the effectiveness of these algorithms.

This paper proposes a motion planner for intelligent vehicles in real time. The motion planner can adaptively sample a number of states according to the initial state of the intelligent vehicle and road geometry. Then a novel method based on the state-space trajectory-generation method generates kinematically feasible trajectories which connected the initial state and the sampled states in a fast manner. At last, the final trajectories will be selected by a defined performance function. The experimental results demonstrate that proposed motion planner has an improvement in generating feasible trajectories. The average runtime of our method is approximately 5% of that of model-based predictive state-space trajectory-generation method. Moreover, our motion planner has the capability to deal with complex traffic environments in real time.