Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging nonconvex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a Linear Program. This reformulation enables us to address motion planning as a Mixed Integer Linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum as fast as 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots.

Control of wire-borne underactuated brachiating robots requires a robust feedback control design that can deal with dynamic uncertainties, actuator constraints and unmeasurable states. In this paper, we develop a robust feedback control for brachiating on flexible cables, building on previous work on optimal trajectory generation and time-varying LQR controller design. We propose a novel simplified model for approximation of the flexible cable dynamics, which enables inclusion of parametric model uncertainties in the system. We then use semidefinite programming (SDP) and sum-of-squares (SOS) optimization to synthesize a time-varying feedback control with formal robustness guarantees to account for model uncertainties and unmeasurable states in the system. Through simulation, hardware experiments and comparison with a time-varying LQR controller, it is shown that the proposed robust controller results in relatively large robust backward reachable sets and is able to reliably track a pre-generated optimal trajectory and achieve the desired brachiating motion in the presence of parametric model uncertainties, actuator limits, and unobservable states.

This paper describes the dynamic modeling and locomotion control of a two-link underactuated brachiating robot traversing a flexible cable. A multi-body system comprised of a two-link robot, a flexible cable, and coupling soft junctions is modeled dynamically. This model is used to formulate an energy-minimizing optimal control strategy that includes the effects of cable vibration induced by robot locomotion. Optimized trajectories and control torque profiles are obtained via multiple-shooting and parametric trajectory approaches. Simulation results show that these optimal torque profiles result in energy-efficient continuous brachiation over a flexible cable. Additional studies examine how the optimal torque profiles change depending on the robot's initial position along a catenary cable.

A novel brachiating robot design is presented for the purpose of traversing elevated wire networks. The robot is capable of moving along a single wire and between parallel wires, thereby enabling traversal of a two-dimensional space. Several novel features distinguish this design compared to previous brachiating robots. These include the ability to transition to and from both “rope” and “ladder” brachiation modes through an integrated wrist, a locking hand design for minimal power consumption, and distributed electronics packages that communicate wirelessly. A payload mounting point is installed, offering space for a variety of remote sensing packages. Experimental results using a prototype robot demonstrate that the system can reliably brachiate along a single wire, and can also reliably perform a swing-up maneuver after failed swing attempts or when transitioning between the rope and ladder locomotion modes. Energy expenditure for a single swing is quantified using experimental data. Overall, the proposed robot design is shown to provide a promising platform for traversal of wire networks in two dimensions.

This paper is an improvement of our previous work [1]. It provides a robust, fast and accurate solution for the inverse kinematics problem of generic serial manipulators - i.e. any number and any combination of revolute and prismatic joints. Here, we propose further enhancements by applying an evolutionary approach on the previous architecture and explore the effects of different parameters on the performance of the algorithm. The algorithm only requires the Denavit-Hartenberg (D-H) representation of the robot as input and no training or robot-dependent optimization function is needed. In order to handle singularities and to overcome the possibility of multiple paths in redundant robots, our approach relies on the computation of multiple (parallel) numerical estimations of the inverse Jacobian while it selects the current best path to the desired configuration of the end-effector using an evolutionary algorithm. But unlike other iterative methods, our method achieves submillimeter accuracy in 20 iterations in average. The algorithm was implemented in C/C++ using POSIX threads, and it can be easily expanded to use more threads and/or many-core GPUs. We demonstrate the high accuracy and real-time performance of our method by testing it with five different robots including a 7-DoF redundant robot. Results show that the evolutionary implementation of the algorithm is able to reduce the number of iterations compared to the previous method significantly, while also finding the solution within the specified margin of error.

We propose a robust and fast solution for the inverse kinematic problem of general serial manipulators - i.e. any number and any combination of revolute and prismatic joints. The algorithm only requires the Denavit-Hartenberg (D-H) representation of the robot as input and no training or robot-dependent optimization function is needed. In order to handle singularities and to overcome the possibility of multiple paths in redundant robots, our approach relies on the computation of multiple (parallel) numerical estimations of the inverse Jacobian while it selects the current best path to the desire configuration of the end-effector. But unlike other iterative methods, our method achieves sub-millimeter accuracy in 20.48ms in average. The algorithm was implemented in C/C++ using 16 POSIX threads, and it can be easily expanded to use more threads and/or many-core GPUs. We demonstrate the high accuracy and the real-time performance of our method by testing it with five different robots, at both non-singular and singular configurations, including a 7-DoF redundant robot.