Modular robots can be rapidly reconfigured into customized articulated legged morphologies capable of mobile manipulation and inspection. However, current gait generation methods do not keep pace with the speed of physical reconfiguration. This work focuses on quickly creating gaits for modular legged robots. We build on a recent method that uses trajectory optimization to design quasi-static gaits given only robot geometry and foot contact patterns. We develop methods to automatically generate contact patterns for new gaits and transitions between them. We show the utility of these methods applied to robots with many limbs, such that limbs can be fluidly reassigned to locomotion, manipulation, or inspection tasks, or to adapt gaits to hardware failures online. We demonstrate gait and transition generation with our modular hexapod and dodecapod robots. The robots switch between gaits that use all limbs for locomotion and those that leave some limbs free to pick up objects or position a camera.

This paper presents experimental results from the real-time parameter estimation of a system model and subsequent trajectory optimization for a dynamic task using the Baxter Research Robot from Rethink Robotics. An active estimator maximizing Fisher information is used in real time with a closed-loop, nonlinear control technique known as sequential action control. Baxter is tasked with estimating the length of a string connected to a load suspended from the gripper with a load cell providing the single source of feedback to the estimator. Following the active estimation, a trajectory is generated using the trep software package that controls Baxter to dynamically swing a suspended load into a box. Several trials are presented with varying initial estimates showing that the estimation is required to obtain adequate open-loop trajectories to complete the prescribed task. The result of one trial with and without the active estimation is also shown in the accompanying video.

This paper presents a new model-based algorithm that computes predictive optimal controls online and in a closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive, underactuated, and constrained systems using only high-level models and trajectory goals. Rather than iteratively optimizing finite horizon control sequences to minimize an objective, this paper derives a closed-form expression for individual control actions, i.e., control values that can be applied for short duration, that optimally improve a tracking objective over a long time horizon. Under mild assumptions, actions become linear feedback laws near equilibria that permit stability analysis and performance-based parameter selection. Globally, optimal actions are guaranteed existence and uniqueness. By sequencing these actions online, in receding horizon fashion, the proposed controller provides a min-max constrained response to a state that avoids the overhead typically required to impose control constraints. Benchmark examples show that the approach can avoid local minima and outperform nonlinear optimal controllers and recent case-specific methods in terms of tracking performance and at speeds that are orders of magnitude faster than traditionally achievable ones.

This paper presents a method for shared control where real-time bursts of optimal control assistance are applied by an observer on-demand to aid a simulated figure in maintaining balance. The proposed Assistive Controller (AC) calculates the optimal burst control fast, in real time, while accounting for nonlinearities of the dynamic model. The short duration of the AC signals allows a rapid transfer of control authority between the nominal and the assistive controller. This scheme avoids prolonged loss of nominal control authority on the part of the figure while facilitating the real-time integration of an external observer's guidance through the assistive control. We demonstrate the benefits of this control scheme in simulation using the Robot Operating System (ROS), in a context where the nominal controller fails to stabilize the figure and the AC is activated intermittently to not only keep it from falling but to additionally push it back to the upright position. The example signifies the efficiency of the proposed model-based AC even in the absence of force/pressure sensors. This approach presents an opportunity for using exoskeletons in balance support, fall prevention, and therapy. In particular, our simulation results indicate that a therapist equipped with an AC interface can, with minimal effort, increase active participation on the part of the patient while ensuring their safety.

This paper presents the details and experimental results from an implementation of real-time trajectory generation and parameter estimation of a dynamic model using the Baxter Research Robot from Rethink Robotics. Trajectory generation is based on the maximization of Fisher information in real-time and closed-loop using a form of Sequential Action Control. On-line estimation is performed with a least-squares estimator employing a nonlinear state observer model computed with trep, a dynamics simulation package. Baxter is tasked with estimating the length of a string connected to a load suspended from the gripper with a load cell providing the single source of feedback to the estimator. Several trials are presented with varying initial estimates showing convergence to the actual length within a 6 second time-frame.

This paper presents a method to develop trajectories which remain optimally insensitive to sudden changes in dynamics. The approach is applied to two example systems that model a vehicle's attempt to navigate through potentially hazardous areas of the state space. Through these simplified examples, we show how to automatically plan trajectories which either avoid or adjust controls to safely pass through critical regions of the state space.