Optimal Control of Mixed Logical Dynamical Systems with Long-Term Temporal Logic Specifications

We present a mathematical programming-based method for control of large a class of nonlinear systems subject to temporal logic task specifications. We consider Mixed Logical Dynamical (MLD) systems, which include linear hybrid automata, constrained linear systems, and piecewise affine systems. We specify tasks using a fragment of linear temporal logic (LTL) that allows both finite- and infinite-horizon properties to be specified, including tasks such as surveillance, periodic walking, repeated assembly, and environmental monitoring. Our method directly encodes an LTL formula as mixed-integer linear constraints on the MLD system, instead of computing a finite abstraction. This approach is efficient; for common tasks the formulation may use significantly fewer binary variables than related approaches. In simulation, we solve non-trivial temporal logic motion planning tasks for high-dimensional continuous systems using our approach

Equality Constrained Differential Dynamic Programming

International audienceTrajectory optimization is an important tool in task-based robot motion planning, due to its generality and convergence guarantees under some mild conditions. It is often used as a post-processing operation to smooth out trajectories that are generated by probabilistic methods or to directly control the robot motion. Unconstrained trajectory optimization problems have been well studied, and are commonly solved using Differential Dynamic Programming methods that allow for fast convergence at a relatively low computational cost. In this paper, we propose an augmented Lagrangian approach that extends these ideas to equality-constrained trajectory optimization problems, while maintaining a balance between convergence speed and numerical stability. We illustrate our contributions on various standard robotic problems and highlights their benefits compared to standard approaches

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

Automated sequence and motion planning for robotic spatial extrusion of 3D trusses

While robotic spatial extrusion has demonstrated a new and efficient means to fabricate 3D truss structures in architectural scale, a major challenge remains in automatically planning extrusion sequence and robotic motion for trusses with unconstrained topologies. This paper presents the first attempt in the field to rigorously formulate the extrusion sequence and motion planning (SAMP) problem, using a CSP encoding. Furthermore, this research proposes a new hierarchical planning framework to solve the extrusion SAMP problems that usually have a long planning horizon and 3D configuration complexity. By decoupling sequence and motion planning, the planning framework is able to efficiently solve the extrusion sequence, end-effector poses, joint configurations, and transition trajectories for spatial trusses with nonstandard topologies. This paper also presents the first detailed computation data to reveal the runtime bottleneck on solving SAMP problems, which provides insight and comparing baseline for future algorithmic development. Together with the algorithmic results, this paper also presents an open-source and modularized software implementation called Choreo that is machine-agnostic. To demonstrate the power of this algorithmic framework, three case studies, including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure

Fast Manipulability Maximization Using Continuous-Time Trajectory Optimization

A significant challenge in manipulation motion planning is to ensure agility in the face of unpredictable changes during task execution. This requires the identification and possible modification of suitable joint-space trajectories, since the joint velocities required to achieve a specific endeffector motion vary with manipulator configuration. For a given manipulator configuration, the joint space-to-task space velocity mapping is characterized by a quantity known as the manipulability index. In contrast to previous control-based approaches, we examine the maximization of manipulability during planning as a way of achieving adaptable and safe joint space-to-task space motion mappings in various scenarios. By representing the manipulator trajectory as a continuous-time Gaussian process (GP), we are able to leverage recent advances in trajectory optimization to maximize the manipulability index during trajectory generation. Moreover, the sparsity of our chosen representation reduces the typically large computational cost associated with maximizing manipulability when additional constraints exist. Results from simulation studies and experiments with a real manipulator demonstrate increases in manipulability, while maintaining smooth trajectories with more dexterous (and therefore more agile) arm configurations.Comment: In Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS'19), Macau, China, Nov. 4-8, 201

Learning Singularity Avoidance

With the increase in complexity of robotic systems and the rise in non-expert users, it can be assumed that task constraints are not explicitly known. In tasks where avoiding singularity is critical to its success, this paper provides an approach, especially for non-expert users, for the system to learn the constraints contained in a set of demonstrations, such that they can be used to optimise an autonomous controller to avoid singularity, without having to explicitly know the task constraints. The proposed approach avoids singularity, and thereby unpredictable behaviour when carrying out a task, by maximising the learnt manipulability throughout the motion of the constrained system, and is not limited to kinematic systems. Its benefits are demonstrated through comparisons with other control policies which show that the constrained manipulability of a system learnt through demonstration can be used to avoid singularities in cases where these other policies would fail. In the absence of the systems manipulability subject to a tasks constraints, the proposed approach can be used instead to infer these with results showing errors less than 10^-5 in 3DOF simulated systems as well as 10^-2 using a 7DOF real world robotic system

Beyond Reynolds: A Constraint-Driven Approach to Cluster Flocking

In this paper, we present an original set of flocking rules using an ecologically-inspired paradigm for control of multi-robot systems. We translate these rules into a constraint-driven optimal control problem where the agents minimize energy consumption subject to safety and task constraints. We prove several properties about the feasible space of the optimal control problem and show that velocity consensus is an optimal solution. We also motivate the inclusion of slack variables in constraint-driven problems when the global state is only partially observable by each agent. Finally, we analyze the case where the communication topology is fixed and connected, and prove that our proposed flocking rules achieve velocity consensus.Comment: 6 page