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Cyclic motions are fundamental patterns in robotic applications, including industrial manipulation and robot locomotion. This article proposes an approach for the online modulation of cyclic motions in robotic applications. For this purpose, we present an integrated programmable central pattern generator (CPG) for the online generation of the reference joint trajectory of a robotic system out of a library of desired periodic motions. The reference trajectory is then followed by the lower level controller of the robot. The proposed CPG generates a smooth reference joint trajectory convergence to the desired one while preserving the position and velocity joint limits of the robot. The proposed CPG consists of one novel bounded output programmable oscillator. We design the programmable oscillator for encoding the desired multidimensional periodic trajectory as a stable limit cycle. We also use the state transformation method to ensure that the oscillator’s output and its first time-derivative preserve the joint position and velocity limits of the robot. With the help of Lyapunov-based arguments, we prove that the proposed CPG provides the global stability and convergence of the desired trajectory. The effectiveness of the proposed CPG for trajectory generation is shown in a passive rehabilitation scenario on the Kuka iiwa robot arm, and also in walking simulation on a seven-link bipedal robot. [ABSTRACT FROM AUTHOR]

This article addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical. This problem is subject to the “curse of dimensionality” associated with the dynamic programming method. This article proposes a novel decoupled data-based control (D2C) algorithm that addresses this problem using a decoupled, “open-loop–closed-loop,” approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, closed-loop control is developed around this open-loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed-loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests a significant reduction in training time compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

We consider the framework of transfer-entropy-regularized Markov decision process (TERMDP) in which the weighted sum of the classical state-dependent cost and the transfer entropy from the state random process to the control input process is minimized. Although TERMDPs are generally formulated as nonconvex optimization problems, an analytical necessary optimality condition can be expressed as a finite set of nonlinear equations, based on which an iterative forward–backward computational procedure similar to the Arimoto–Blahut algorithm is developed. It is shown that every limit point of the sequence generated by the proposed algorithm is a stationary point of the TERMDP. Applications of TERMDPs are discussed in the context of networked control systems theory and nonequilibrium thermodynamics. The proposed algorithm is applied to an information-constrained maze navigation problem, whereby we study how the price of information qualitatively alters the optimal decision polices. [ABSTRACT FROM AUTHOR]

Many safety-critical systems, such as autonomous vehicles and service robots, must achieve high-level task specifications with performance guarantees. Much recent progress toward this goal has been made through an automatic controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of the state space, deal only with a convex fragment of temporal logic, or are not provably complete. We propose a scalable, provably complete algorithm that synthesizes continuous trajectories to satisfy nonconvex temporal logic over reals (RTL) specifications. We separate discrete task planning and continuous motion planning on-the-fly and harness highly efficient Boolean satisfiability and linear programming solvers to find dynamically feasible trajectories that satisfy nonconvex RTL specifications for high-dimensional systems. The proposed design algorithms are proven sound and complete, and simulation results demonstrate our approach's scalability. [ABSTRACT FROM AUTHOR]

A new approach for trajectory optimization of musculoskeletal dynamic models is introduced. The model combines rigid-body and muscle dynamics described with a Hill-type model driven by neural control inputs. The objective is to find input and state trajectories that are optimal with respect to a minimum-effort objective and meet constraints associated with musculoskeletal models. The measure of effort is given by the integral of pairwise average forces of the agonist-antagonist muscles. The concepts of flat parameterization of nonlinear systems and sum-of-squares optimization are combined to yield a method that eliminates the numerous set of dynamic constraints present in collocation methods. With terminal equilibrium, optimization reduces to a feasible linear program, and a recursive feasibility proof is given for more general polynomial optimization cases. The methods of the article can be used as a basis for fast, and efficient solvers for hierarchical, and receding-horizon control schemes. Two simulation examples are included to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]